Research Article Fiber-Reinforced Polymer-Packaged Optical...

Research ArticleFiber-Reinforced Polymer-Packaged Optical Fiber Bragg GratingStrain Sensors for Infrastructures under Harsh Environment

Zhi Zhou Zhenzhen Wang and Lian Shao

Institute of Smart Structures Dalian University of Technology Ganjingzi Liaoning Dalian 116024 China

Correspondence should be addressed to Zhi Zhou zhouzhidluteducn

Received 8 June 2016 Accepted 3 August 2016

Academic Editor Rafael Morales

Copyright copy 2016 Zhi Zhou et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Optical fiber Bragg grating (FBG) has been recognized as an outstanding high-performance local monitoring sensor and islargely applied in structural health monitoring (SHM) This paper proposes a series of fiber-reinforced polymer- (FRP-) packagedoptical fiber Bragg grating strain sensors to completely meet the requirements of rough civil engineering infrastructures and theirsensing performance under normal environment and harsh environment is experimentally investigated It is experimentally andtheoretically proved that FRP-packaged FBG strain sensors maintain excellent sensing performance as the bare FBG sensor under aharsh environment and their durability is significantly enhanced due to the FRPmaterialsThese FRP-packaged FBG strain sensorsare successfully applied in the SHM system of Aizhai Bridge

1 Introduction

Infrastructures such as long-span bridges high-rise build-ings large dams nuclear power stations and offshore plat-forms will inevitably suffer damage accumulation and resis-tance degradation subjected to coupling actions of environ-mental corrosion material aging long-term loading fatigueand natural disaster hazards even collapse during their longtime of service [1] Therefore in order to assure structuralsafety integrity suitability and durability a lot of infras-tructures in service are in great need for intelligent healthmonitoring systems to evaluate their safety and rehabilitateand further control their damage Due to the frequentdisastrous lessons more and more infrastructures have beenequipped with long-term health monitoring systems duringconstruction [2] As one of the most important inventions inthe measurement field in the late 20th century optical fiberBragg grating (FBG) has been greatly recognized and largelyapplied in long-term structural healthmonitoring (SHM)dueto the fact that optical FBG shows distinguishing advantageselectromagnetic resistance small size resistance to corrosionand so forth [3ndash11] Fiber Bragg grating sensors furtherprovide an absolute measurement that exhibits minimaldrift with time which performs measurement at a discreteposition in the fiber and several sensors can be multiplexed

for a complex network connected to a single interrogatoralong a single fiber As the main ingredient of the bareoptical fiber is SiO2 and the outer diameter is only 125 120583mthe shear capacity of the optical fiber is so poor Due to itsfragility it is rather difficult to be applied directly in the roughcivil engineering infrastructures and harsh environmentswithout packaging Therefore it is an important issue todevelop packaging techniques for bare FBG strain sensorswhich can be well protected inside the matrix componentand less likely to be damaged by external infringement Thekey problem of this development focuses on the selectionof packaging materials for sensors form of different layoutprocess and performance requirements in order to ensurethe that packaged FBG sensor possesses excellent durabilitylinearity repeatability andmeasurement range for long-termmonitoring of civil engineering There are three solutionsfor realizing the combination of FBG sensors and packagingmaterials Firstly metallic materials can be chosen as thepackaging materials to combine with FBG sensors by anadhesive interlayer Because of the plastic properties underlarge strain conditions and corrosion of metallic materialsas well as the creep and aging characteristics of the adhesiveinterlayer sensors developed by this encapsulation techniqueare deficient in durability linearity and repeatability inaddition to the small measurement scale (less than 2000120583120576)

Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 3953750 18 pageshttpdxdoiorg10115520163953750

2 Journal of Sensors

Secondly the FBG sensors are firstly clamped with the endedmechanical anchorage and then packaged by the additionalprotection It is inevitable that the creep of OFBG sensorswould occur under sustained loads due tomechanical clamp-ing therefore the measurement scale is just as the ultimatestrain of the FBG sensor In addition to this the durabilityis restricted by the material of the clamping devices Thirdlyadvanced composites can be introduced as packagingmateri-als such as fiber-reinforced polymer (FRP) including carbonfiber-reinforced polymer (CFRP) aramid fiber-reinforcedpolymer (AFRP) basalt fiber-reinforced polymer (BFRP)and glass fiber-reinforced polymer (GFRP) FRP compositesare originated from the design of large high-performancestructures in the aerospace industry A fundamental issuein the implementation of an OFBG-based SHM system incomposite structures aerospace area is the embedment ofsensors during manufacturing Tsutsui et al applied small-diameter optical fiber sensors to stiffened composite panelsfor the detection of impact damage [12] Ryu et al haveused multiplexed and multichanneled built-in FBG sensorsto monitor the buckling behavior of a composite wing box[13] Takeda et al used FBG sensors to monitor damage dueto compressive load in CFRP stiffened panels [14] Tserpeset al developed an integrated methodology for monitoringstrain and damage in CFRP fuselage panels and embedmentof fiber sensors in the panel during manufacturing was doneso as tominimize risk of fiber breaking duringmanufacturingand impact testing and to effectively capture strains beingrepresentative of the damage developed in the panel [15]

In this paper the bonding mechanism of the combi-nation of FRP and FBG sensors is explored firstly Andthen an experiment program is conducted for investigatingthe durability properties of BFRP bars and GFRP barswhich are used as typical encapsulation materials Thirdlyseries of FRP-packaged FBG strain sensors are developed forinfrastructures under harsh environment and their sensingperformance under normal environment and harsh envi-ronment is experimentally investigated Finally the practicalapplication of these FRP-packaged FBG strain sensors inAizhai Bridge SHM system is briefly introduced

2 Bonding Mechanism betweenFRP and FBG Sensors

As we know the sensing properties of FRP-packaged opticalfiber strain sensors are determined by the FBG and packagingmaterials Due to the small proportion of FBG the basicsensing performance properties such as linearity repeatabil-ity and measurement scale and the main durability indexare directly influenced by the basic mechanical and chemicalproperties of packaging materials Fiber-reinforced polymercomposites provide a reliable means for the developmentof high-performance packaged optical fiber strain sensorsowing to their linear-elastic material constitutive propertiesnamely the notion that the elastic modulus remains con-stant until failure (as shown in Figure 1) excellent fatigueperformance and durability Particularly for that the whole-process pseudoelasticity of FRP composites ensures the per-fect linearity and repeatability of the FRP-packaged optical

CFRP1CFRP2

CFRP-OFBG1CFRP-OFBG2

Strain (120583120576)5000450040003500300025002000150010005000

0

100

200

300

400

500

600

700

Stre

ss (M

Pa)

Figure 1 The constitutive curve of CFRP bar

fiber strain sensors in the whole measurement scale Thefundamental basis of taking FRP composites as packagingmaterials is further explained as follows

21 The Compatibility between FBG and FRP CompositesFrom the point of view of material component fiber-reinforced polymer composites commonly consist of glassfibers (or carbon fibers aramid fibers basalt fiber andhybrid fiber) resins additives and so forth Silica as thebasic composition of the optical fiber is also the mainmaterial composition of glass fibers Thus the glass fibers areinfiltrated in the resin and cure for molding easily which isthe same as optical fibers It is shown from the SEM photo(Figure 2) of bare FBG and FRP that the bare fiber FRPcombined well with FRP composites and worked together inthe manner of full interaction

22 Effect of FRP on the SensingCharacteristics of FBGSensorsThe main indexes of sensing elements are highlighted inlinearity measurement range repeatability and so forth andthe macroscopic constitutive property of FRP materials isjust linear elastic which ensures that the excellent linearityof the FBG sensor would be maintained after encapsulatingIn addition to that the FBG is precompressed and inducedby the shrinkage of the resin in the curing process ofthermosetting FRP composites due to their perfect bondingwith FRP composites and the precompressed section willbe the extended portion for the tensile strain measurementrange compared with the bare FBG sensor under the initiallyunstressed state According to the experiment results shownin Figure 3 the range of GFRP-packaged FBG sensor canreach up to 7000sim8000120583120576 By contrast the range of bareFBG sensors is only 3000sim4000 120583120576 Thus it can be seen thatFRP composites increase the measurement scale significantlywithout changing the sensing performance of the FBG sensor(Figure 5)

Journal of Sensors 3

(a) The interface of bare FBG and CFRP (b) The interface of bare FBG and CFRP

Figure 2 SEM photo of bare FBG and FRP

Protecting layer

Optical fiber

Adhesive layer

Host materials

o

2Lf

raprh

rc x

(a)

Protecting layer

Optical fiber

Adhesive layer

Host materials

uh(x)

uc(x)

Δa(x)

Δp(x)

(b)

Figure 3 Cylindrical model of optical fiber strain sensing and relationship of deformation


23 Strain Transfer of the FRP-Packaged Optical Fiber StrainSensors Embedded FRP-packaged FBG sensors are usuallyconstituted by FRP encapsulation layer and sensing fiberDeformation of host materials induced by external actionpasses through FRP encapsulation layer at first and thenarrives at the FBG sensor with a part of strain consumed bythe FRP encapsulation layer in the strain transferring processwhich causes the strain transfer error between the targetstrain of structures 120576ℎ(0) and measurement of FBG sensors120576119888(119909) In order to estimate the error between themeasurementof FBG sensors and the strain of structures as well ascorrecting the strain transfer error and improving the testingaccuracy of sensors a cylinder within the effective workinglength of optical fibers consisting of optical fiber protectinglayer adhesive layer and host materials was chosen as themechanical analysis model to investigate the strain transfermechanism in optical fiber sensing Basic assumptions wereintroduced as follows (1) optical fiber protecting layeradhesive layer and host materials were considered to belinear elastic and isotropic (2) all of the adhesive interfaceswere continuous and satisfied the deformation compatibilitycondition (3) temperature effects were ignored (4) opticalfiber is not sensitive to lateral stress and thus the lateral stressand shear stress were ignored According to the hypothesis ofdisplacement continuity the displacement at arbitrary pointin the cylindrical model can be expressed as in the followingformula

119906 (119909) =

119906119888 (119909) 0 le 119903 le 119903119888119906119901 (119903 119909) 119903119888 lt 119903 le 119903119886119901119906119886 (119903 119909) 119903119886119901 lt 119903 le 119903ℎ119906ℎ (119909) 119903 gt 119903ℎ

(1)

In formula (1) 119906119888(119909) 119906119901(119903 119909) 119906119886(119903 119909) and 119906ℎ(119909) are rep-resented as the displacement of the optical fiber protectinglayer adhesive layer and host materials respectivelyThe dis-placement compatibility equations at the adhesive interfaceare shown in formula (2) Due to the presence of the pro-tective layer and adhesive layer there is relative displacementbetween the optical fiber and hostmaterials which is inducedby the shear deformation of the protective layer and theadhesive layerThe quantity relationships between the relativedisplacement for the optical fiber and host materials andshear deformation in the protective layer and the adhesivelayer are given in formulas (3)sim(5)The relative displacementat each interface is shown in Figure 3(b) Hence

119906119888 (119909) = 119906119901 (119903119888 119909)119906119901 (119903119888 119909) = 119906119886 (119903119888 119909)119906119886 (119903119888 119909) = 119906ℎ (119909)

(2)

119906ℎ (119909) minus 119906119888 (119909) = Δ 119886 (119909) + Δ119901 (119909) (3)

119906119886 (119903ℎ 119909) minus 119906119886 (119903119886119901 119909) = Δ 119886 (119909) (4)

119906119901 (119903119886119901 119909) minus 119906119901 (119903119888 119909) = Δ119901 (119909) (5)

When 119909 = 0120576119888 (119903 0) = 120576119886 (119903 0) = 120576119886119901 (119903 0) = 120576ℎ (119903 0) (6)

The axial force equilibria for the optical fiber infinitesimalprotecting layer infinitesimal and adhesive layer infinitesimalare shown in Figures 4(a)ndash4(c) and the axial force equilib-rium equations are

sum119865119909 = 0 (7)

119889120590119888 (119909)119889119909 = minus2120591119901119888 (119903119888 119909)119903119888 (8)

119889120590119901 (119909)119889119909 = 2 [120591119901119888 (119903119888 119909) 119903119888 minus 120591119886119901 (119903119886119901 119909) 119903119886119901]1199032119886119901 minus 1199032119888 (9)

119889120590119886 (119909)119889119909 = 2 [120591119886119901 (119903119886119901 119909) 119903119888 minus 120591ℎ (119903ℎ 119909) 119903ℎ]1199032ℎminus 1199032119886119901 (10)

Deformation compatibility equations in the protective layerand adhesive layer can be approximately expressed as [16]

120591 (119903 119909) = 119903119886119901119903 120591119886119901 (119903119886119901 119909) 119903119888 le 119903 le 119903119886119901120591 (119903 119909) = 119903ℎ119903 120591ℎ (119903ℎ 119909) 119903119886119901 le 119903 le 119903ℎ

(11)

When 119903 = 119903119888 and 119903 = 119903119886119901119889120590119901 (119909)119889119909 = 0119889120590119886 (119909)119889119909 = 0

(12)

Therefore

120590119901 (119909) = cons tan 119905120590119886 (119909) = cons tan 119905 (13)

Physical equations and geometric equations for optical fiberprotecting layer and adhesive layer are as follows

120576ℎ (119909) = 120590ℎ (119909)119864ℎ120576119888 (119909) = 120590119888 (119909)119864119888

120574119886 (119903 119909) = 120591 (119903 119909)119866119886 119903119886119901 le 119903 le 119903ℎ120574119901 (119903 119909) = 120591 (119903 119909)119866119901 119903119888 le 119903 le 119903119886119901

(14)


r

120590c(x)120591pc(rc x)

120591pc(rc x)

120590c(x) + d120590c(x)

x

rc

dx

(a) FBG

r

120590p(x)

120590p(x)

120591ap(rap x) 120590p(x) + d120590p(x)

xrcrap

120591pc(rpc x)120590p(x) + d120590p(x)

120591ap(rap x)

(b) Protecting layer

120591ap(rap x)

r

120590a(x)

120590a(x)

120591pc(rpc x)120590a(x) + d120590a(x)

xrhrap

120591ap(rap x)

120590a(x) + d120590a(x)

120591pc(rpc x)

dx

(c) Adhesive layer

Figure 4 Schematic diagram of an infinitesimal

Strain (120583120576)

LoadingUnloading

80006000400020000

0006

0004

0002

0000

Δ120582

120582

(a) The strain sensing sensitivity of OFBG-GFRP bars

LoadingUnloading

0006

0004

0002

0000

Δ120582

120582

2000 4000 6000 80000

Strain (120583120576)

(b) The range and repeatability of OFBG-GFRP bars

Figure 5 The effect of FRP on FBG


Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)

Formula (16) can be derived by means of substituting for-mulas (11) and (15) into formula (3) whose first derivativeand second derivative are shown in formulas (17) and (18)respectively The differential equation of interfacial shearstress 120591119886119901(119903119886119901 119909) in formula (18) is obtained based on formula(8) and the assumption that the axial stress of host materials120590ℎ(119909) is considered to be constant in case of short measuredlength

int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)

Therefore formula (18) can be simplified as

1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)

The general solution is obtained as follows

120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)

The axial force of the optical fiber can be expressed as follows

119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)

Introducing formula (21) into formula (24) the axial force ofthe optical fiber can be expressed in the following

119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)

On the basis of formula (6) and the axial force of the opticalfiber being zero at 119909 = 119897119891 the following boundary conditionsare introduced to calculate integration constants 119860 and 119861

119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)

Thus the interfacial shear stress can be obtained as follows

120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]

= 120576ℎ (0) times [1 minus sh (120582119909)sh (120582119897119891)]

(28)

In (28) 120576ℎ(0) is the axial strain of the host material at 119909 = 0This is the generic expression of strain transfer mecha-

nism for the embedded optical fiber sensors as for embeddedFRP-OFBG strain sensors adjustments shown as followsshould be made with specific application 119903119886119901 rarr 119903119888 119866119886 rarr119866FRP therefore formula (19) is converted to the followingformula

12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)

We defined the average strain measurement of FBG sensors120576119888(119909) and the average strain of structures 120576ℎ(119909)The interfacial


Table 1 Interlaminar shear strength of BFRP and GFRP rebar under salt and acid condition under different age

FRP bars Corrosion solution Items 20 days 240 days

BFRP

SaltAverage value 451 312

Variance 22 25Deterioration rate minus98 minus376

AcidAverage value 433 294


Blank specimen Interlaminar shear strength (MPa) 50Variance (MPa) 15

GFRP






strain transferring error rate 120578 and the error correction factor119896 are expressed as follows

120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891

120578 = 1003816100381610038161003816120576119888 (119909) minus 120576ℎ (119909)1003816100381610038161003816120576ℎ (119909) = cosh (1205821119871119891) minus 11205821119871119891 sinh (1205821119871119891)

119896 = 11 minus 120578

(30)

In (29) 119866FRP is the shear modulus of the FRP composites 119864119888is the elastic modulus of the optical FBG 119903ℎ is the distancebetween optical fiber and matrix material 119903119888 is the outerdiameter of the optical fiber 2119871119891 is the effective workinglength of the optical fiber

Calculations proved that the interfacial strain transferringerror rate of CFRP-OFBG bars for the shear modulus beinggreater than 12GPa and the outer diameter being Φ4simΦ10mm is 192sim216 and the corresponding error correc-tion factor 119896 is 102sim1022 By contrast the interfacial straintransferring error rate of GFRP-OFBG bars for the shearmodulus being greater than 49GPa and the outer diameterbeingΦ4simΦ10mm is 311sim35 and the corresponding errorcorrection factor 119896 is 1034sim1036 From the results providedin this section we can conclude that the test accuracy ofFRP-packaged optical fiber strain sensors is sufficient forcivil engineering structures with significant material discretecharacteristic and can be applied in the practical structuresdirectly without any error correction

3 Corrosion Durability Test of the FRP Bars

Corrosion durability tests of the GFRP bars and BFRP barsunder the condition of acid and alkali salt were conductedin this section with the comparative study of degeneration ofinterlaminar shear properties and tensile properties after cor-rosion The corrosion solution with different ingredient andmixing ratio was exploited to simulate the acid alkali and saltcorrosion environment in the practical civil engineering

31 Variation in Tensile Properties of FRP Bars The ultimatetensile strength and tensile modulus of the BFRP bars andGFRP bars after being corroded in the acid alkali andsalt solution for 20 days and 240 days are summarized inTable 1

The variations of the ultimate tensile strength and tensilemodulus of the BFRP bars and GFRP bars with corrosivetime are presented in Figures 6 and 7 Since BFRP bars wereseverely damaged in the alkali solution in 20 days the tensilestrength of both FRP bars was not measured due to the lackof a control group It is shown that both of the ultimate tensilestrengths increase with the corrosive time in the acid and saltsolution For a particular corrosive time loss of the ultimatetensile strength of BFRP bars is more than that of GFRP barsin either acid solution or salt solution besides loss of theultimate tensile strength in the acid solution is more than inthe salt solution for both of the FRP bars Whereas the tensilemodulus of BFRP bars increases with the corrosive time onthe contrary the tensilemodulus ofGFRPbars decreaseswiththe corrosive time In addition to that the change rate of thetensilemodulus for both FRP bars in the acid solution ismorethan that in the salt solution Although the corrosion damageof basalt fibers does not occur the interface between fibersand the resin is corrosively damaged by the acid solutionand the salt solution which cannot transfer the tension stressbetween fibers effectively inducing stress concentration in aportion of fibers followed by the decrease of ultimate tensile


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)

Figure 6 Curves of tensile strength versus age of BFRP and GFRP rebar under acid and salt condition

250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)

Figure 7 Curves of tensile modulus versus age of BFRP and GFRP rebar under acid and salt condition

strength of BFRP bars In addition the relative slip betweenfibers and resin is also induced by the deterioration of theadhesive interface

32 Variation in Interlaminar Shear Strength of FRP Bars Theinterlaminar shear strength of BFRP and GFRP rebar undersalt and acid condition under different age is summarized inTable 1

The interlaminar shear strength of FRP bars is the impor-tant parameter reflecting the bonding properties between theresin and the fibers throughout the short beam shear test

The interlaminar shear strength of BFRP bars and GFRPbars decreases with corrosive time and degeneration of theinterlaminar shear strength for both FRP bars in the acidsolution is more than that in the salt solution In additionloss of the interlaminar shear strength of BFRP bars is morethan in the GFRP bars in both acid solution and salt solutionThe variation of interlaminar shear strengthmentioned abovereveals the deterioration of the adhesive interface betweenfibers and the resin induced by the corrosive solution asshown in Figure 8


30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()

Corrosive time (d)250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)

Figure 8 Curves of interlaminar shear strength and age in BFRP and GFRP rebar under acid and salt condition

Figure 9 Embeddable FRP-FBG strain sensor

Figure 10 Embeddable FRP strain sensor with fixtures at two ends

Figure 11 Surface-welded FRP strain sensor

4 FRP-Packaged Fiber Bragg Grating (FBG)Strain Sensors

41 Package Structure of FRP-Packaged FBG Strain SensorBased on research achievements on the FRP-OFBG bars(Figures 20 and 21) a series of embedded FRP-packagedfiber Bragg grating strain sensors FRP-packaged fiber Bragg

grating strain sensors with expanding ends surface-weldingFRP-packaged fiber Bragg grating strain sensors long gaugeembedded FRP-packaged fiber Bragg grating strain sensorsand 3D FRP-packaged fiber Bragg grating strain sensors weredeveloped for the demand of engineering test shown asFigures 9ndash13


Figure 12 Long gauge embeddable FRP strain sensor

Figure 13 Three-dimensional FBG-packaged strain sensor

Figure 14 Test of FRP-packaged FBG strain sensor

42 Sensing Performance of FRP-Packaged Fiber GratingStrain Sensors Sensing performance tests in the presentedstudy were conducted on the material testing machineInstron-5569 and the center wavelength of fiber Bragggrating was demodulated by SI-720 produced by MOI com-pany with accuracy of 1 pm Strain of FRP-packaged fibergrating strain sensors was measured by the extensome-ter with the resolution of 1 120583120576 In order to eliminate theeffect on the variation of center wavelength of tempera-ture laboratory temperature was maintained as constantat 25∘C by air conditioning The test setup is shown inFigure 14 3sim5 loading-unloading cycles were conducted oneach type of sensor mentioned earlier and their variationwas recorded in center wavelength and strain respectivelyfor analyzing the sensing performance index shown asFigure 15

It is shown that from the test results the measurementscale of this series of FRP-packaged fiber grating strainsensors is more than 5000120583120576 (the maximum strain can reach12000120583120576) the test accuracy is 1 120583120576 the repeatability is less

than 10 linearity is less than 10 and hysteresis is less than05

43 Sensing Performance of FRP-Packaged FiberGrating Strain Sensors in Harsh Environment

431 Strain Sensing Performance in High-Temperature Envi-ronments The service temperature ranged from minus40∘C to60∘C for most civil engineering structures but higher tem-perature occurs in some structural elements therefore itis meaningful to research the sensing performance of FRP-packaged fiber grating strain sensors under high-temperatureconditions due to the undesirable high temperature perfor-mance of FRP material

This experiment was conducted on the MTS testingmachine as shown in Figure 14 Strain and variation ofcenter wavelength were measured by the high-temperatureextensometer and SI-720 optical fiber grating demodulatorproduced by MOI company and the test setup is shown in


Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading

(a) Direct embedded GFRP-packaged FBG sensors

LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000

(b) Direct embedded CFRP-packaged FBG sensors

Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582

(c) GFRP-packaged FBG sensors with expanding ends

0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading

(d) Surface-welding GFRP-packaged FBG sensors

Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3

(e) Long gauge embedded GFRP-packaged FBG sensors

Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582

(f) Long gauge embedded GFRP-packaged FBG sensors

Figure 15 Properties of the FRP-packaged FBG strain sensors


Figure 16 Test setup of GFRP-packaged FBG at high temperature

Figure 16 In the presented experiment the sensing perfor-mances such as linearity and repeatability at 20∘C 40∘C60∘C 80∘C 100∘C 120∘C and 140∘C which were controlledby the high-temperature furnace were investigated Experi-ment results for one of the testing specimens are shown inFigure 17

It can be seen from the experimental results that thestrain sensitivity of the GFRP-packaged FBG sensors at 40∘C60∘C 80∘C 100∘C 120∘C and 140∘C is around 12 pm120583120576being close to that at 20∘Cnormal environmentTherefore wecan conclude that the performance of FRP-packaged opticalfiber strain sensors does not degenerate under the ambienttemperature of 140∘C

432 Fatigue Performance Experiment of FRP-Packaged Opti-cal Fiber Strain Sensors In order to examine the stabilityand reliability of FRP-packaged optical fiber strain sensorsapplied on the long-term monitoring of civil engineeringstructures fatigue performance experiment of this series ofFRP-packaged optical fiber strain sensors was performed onthe fatigue testing machine MTS-810 with the test frequencyselected as 50Hz For the purpose of accelerating the fatiguetest the strain amplitude was determined as 2000 plusmn 1000 120583120576and 3000 plusmn 1000 120583120576 The center wavelength response of FBGsensors was recorded at intervals of a fixed time in orderto compare variation of that at each moment A significantchange of the center wavelength variation at a momentwith a comparison to that at the initial moment infers thatthe fatigue damage is accumulated in the FRP-packagedoptical fiber strain sensors and this phenomenon couldbe employed to evaluate fatigue reliability of FRP-packagedoptical fiber strain sensors In this paper two surface-weldingGFRP-packaged optical fiber strain sensors and a directembedded CFRP-packaged optical fiber strain sensor wererandomly selected as testing specimens to investigate thesensing performance after high-cycle fatigue besides threeGFRP-packaged optical fiber strain sensors with expandingends were also randomly chosen to examine the sensingperformance after low-cycle fatigue During the experimentthe center wavelengths of FBG sensors were recorded by SI-425 optical fiber grating demodulator produced by MicronOptics company in which the instrument wavelength resolu-tion is 5 pmand scanning frequency is 250HzThe fatigue test

Table 2 The testing results at low cycle fatigue

Specimen Strainamplitude (120583120576) Cycles

(10000 times)Wavelength

variation (nm)Surface weldingGFRP (1) 2000sim3000 100 7

Surface weldingGFRP (2) 2000sim3000 100 9


Direct embeddedCFRP 2000sim3000 100 7

setup is shown in Figure 18 Part of the experiment results ofall the specimens are summarized in Table 2 Figure 19 showssegmenting time history curves of one specimen

We can see from experimental results that there is nostrain decrease of FRP-packaged FBG strain sensors duringthe fatigue test and that no member resistance reduction andno obvious damage occurred during the test After multiplefatigue cycles none of the significant drifts of the fiber gratingcenter wavelength appeared It is shown that FRP compositesprotect the sensing element effectively and the stability ofFRP-packaged FBG strain sensors kept excellent which issuited for civil engineering applications

Moreover the fatigue tests of FRP-packaged FBG strainsensors at high strain amplitude were conducted and acomparison was made between the sensorsrsquo strain sensingperformance after certain fatigue circles and that of thecontrol group In this test the strain amplitude of sensor 1is 3000 plusmn 2000 120583120576 and that of sensor 2 is 4500 plusmn 1500 120583120576 testresults are shown in Figures 20(a)ndash20(d)

It can be seen that FRP-packaged strain sensors whichhave experienced a certain number of fatigue cycles retainthe original strain sensing performance such as good linear-ity and repeatability as well as a longer fatigue life

433 Corrosion Durability Test of FRP-Packaged Optical FiberBragg Grating Strain Sensors In order to verify the sensorrsquosdurability index different types of FRP-packaged optical fiberBragg grating (FBG) strain sensors were placed in salt spraychamber with the working temperature of 35∘C and the salt


Strain (120583120576)

First loadingFirst unloadingSecond loading

Second unloadingFitting

Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C

Figure 17 Relationship between wavelength changes and strain at different temperatures of sensor one


Figure 18 Fatigue test of FRP-packaged FBG strain sensor

Table 3 Monitoring items and technical parameters of FRP-packaged optical fiber Bragg grating sensors

Object Monitoring items Sensors NumbersMethod Frequency Accuracy Scale

Main-beam Steel strain FBG 20Hz 1120583120576 plusmn1000120583120576 40Main-beam Steel temperature FBG 1 timeh 05∘C minus20∘Csim+70∘C 15Main-tower Concrete strain FBG 20Hz 1 120583120576 plusmn1000120583120576 8Main-tower Concrete temperature FBG 1 timeh 05∘C minus20∘Csim+70∘C 8

spray of 35 NaCl solution shown as Figure 21 It can beseen from the results of corrosion test that the corrosionresistance of the metal packaged FBG sensors is far less thanthe FRP-packaged FBG sensors This series of FRP-packagedFBG strain sensors overcomes the insurmountable durabilityissues compared with the traditional adhesive packaged FBGstrain sensors possessing outstanding advantages such assimple laying process in practical engineering large mea-surement scale (more than 5000 120583120576 the maximum can reach10000120583120576) excellent durability high accuracy (1sim2 120583120576) andlow error correction factor Furthermore it can be easilycustomized according to custom

Key performance indicators of the series of FRP-packagedoptical fiber Bragg grating strain sensors are summarizedas follows measurement scale is more than 5000120583120576 testaccuracy is 1 120583120576 repeatability is less than 1 linearity is lessthan 10 hysteresis is less than 05 and so forth No fatigueproperties are found under more than one million times offatigue cycles with strain amplitude of 3000 plusmn 1000 120583120576

This series of FRP-packaged FBG strain sensors is par-ticularly suitable for the internal strain measurement of theconcrete structures besides the whole-process monitoringof civil engineering structures including construction stagecompletion test stage and in-service stage Still it also can beeasily used for road engineering geotechnical engineeringand so forth throughout the reconstruction design

5 Applications in Aizhai Bridge

Aizhai Bridge is a super long suspension bridge with sepa-rated towers and beams and with span arrangement of 242m

+ 1176m + 116m In order to obtain the information onstructure behavior in service a structural health monitoring(SHM) system was established for providing informationabout conditions such as strain temperature accelerationdeflection wind velocity cable force and humidity In thisSHM system surface-welding GFRP-packaged optical fiberstrain and temperature sensors (shown as Figure 9) are usedfor strain and temperature measuring of the main beam andmain tower and the measuring point arrangement is shownin Figure 22 The monitoring items and technical parametersof FRP-packaged optical fiber Bragg grating sensors arelisted in Table 3 The data acquired and processed by FBGdemodulator is transferred to the data receiving server inwhich the data can be retained managed and arithmeticallyprocessed

6 Conclusions

In this study a series of FRP-packaged optical fiber Bragggrating strain sensors to completely meet the requirementsof the rough civil engineering infrastructures are introducedand their sensing performances under normal environmentand harsh environment are experimentally investigated thefollowing conclusions can be drawn

(1) Based on stain transfer mechanism it is theoreticallyproved that the testing accuracy of FRP-packagedoptical fiber strain sensors is sufficient for civil engi-neering structures and can be applied in the practicalstructures directly without any error correction


Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753

Figure 19 Response of the FBG wavelength at different times


The first circle loadingThe first circle unloadingThe second circle loadingThe second circle unloadingFitting

Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)

1 sensor after 45000 times

Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)

Figure 20 In situ diagram of FRP-packaged OFBG sensors installation

(2) FRP composites do not change the sensing perfor-mance of the FBG sensor furthermore the measure-ment scale significantly increased to 8000sim12000120583120576

(3) FRP-packaged optical fiber FBG strain sensors do notdegenerate under the ambient temperature of 140∘Cand maintain excellent linearity and repeatability asthe bare FBG in the case of experiencing a certainnumber of fatigue cycles Besides they have superiorcorrosion resistance compared with metal packagedoptical fiber strain sensors which makes them par-ticularly suitable for the internal strain measurement

of the concrete structures and the whole-processmonitoring for civil engineering structures includingconstruction stage completion test stage and in-service stage

Competing Interests

The authors declare that they have no financial and personalrelationships with other people or organizations that caninappropriately influence this work and that there is noprofessional or other personal interest of any nature or


Figure 21 Schematic diagram of FRP-packaged OFBG sensors installation

121

3000

56800

Temperature compensation

Main-tower strain

Main-tower vibration

Environmental meteorology

Tower top displacement

Cable clip displacement

Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration

Main-beam displacement

Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain


Figure 22 Measuring point arrangement of all kinds of sensors

kind in any product service andor company that could beconstrued as influencing the position presented in or thereview of the manuscript

References

[1] J P Ou ldquoDamage accumulation and safety evaluation forimportant large infrastructuresrdquo in 21st Centuryrsquos ChineseMechanics-9th Science Association Reports of lsquoForum for YouthScientistrsquo pp 179ndash189 Tsinghua University Press BeijingChina 1996

[2] G W Housner L A Bergman T K Caughey et al ldquoStruc-tural control past present and futurerdquo Journal of EngineeringMechanics vol 123 no 9 pp 897ndash971 1997

[3] GMeltzWMorey andWGlenn ldquoFormation of bragg gratingsin optical fibers by a transverse holographic methodrdquo OpticsLetters vol 14 no 15 pp 823ndash825 1989

[4] A A Mufti ldquoFRPs and FOSs lead to innovation in Canadiancivil engineering structuresrdquo Construction and Building Materi-als vol 17 no 6-7 pp 379ndash387 2003

[5] Z Zhou T Graver and J P Ou ldquoTechniques of advancedFBG sensors manufacturing demodulation encapsulation andtheir application in the structural healthmonitoring of bridgesrdquoPacific Science Review vol 5 no 1 pp 116ndash121 2003

[6] Z Zhou B Wang and J P Ou ldquoLocal damage detectionof RC structures with distributive FRP-OFBG sensorsrdquo inProceedings of the 2nd International Workshop on StructuralHealth Monitoring of Innovative Civil Engineering Structuresvol 22-23 pp 205ndash214 Winnipeg Canada September 2004

[7] Z Zhou and J P Ou ldquoDevelopment of FBG sensors for Struc-tural Health Monitoring in civil infrastructuresrdquo in Proceedingof the North American Euro-Pacific Workshop lsquoSensing Issues

in Civil Structural Health Monitoringrsquo Waikiki Hawaii USA2004

[8] Z Zhou C G Lan and J P Ou ldquoA novel ice-pressure sensorbased on dual FBGsrdquo in Smart Structures and Materials 2005Sensors and Smart Structures Technologies for Civil Mechanicaland Aerospace Systems vol 5765 of Proceedings of SPIE SanDiego Calif USA 2005

[9] Z Zhou J Liu H Li and J Ou ldquoA new kind of high durabletraffic weighbridge based on FBG sensorsrdquo in 17th InternationalConference on Optical Fibre Sensors vol 5855 of Proceedings ofSPIE pp 735ndash738 Bruges Belgium May 2005

[10] J P Ou and Z Zhou ldquoTechniques of optical fiber Bragggrating smart sensors and intelligent monitoring systems ofinfrastructuresrdquo in Proceedings of the 1st InternationalWorkshopon Advanced Smart Materials and Smart Structures Technologyp 23 Honolulu Hawaii USA June 2003

[11] Z Zhou J P Ou and B Wang ldquoSmart FRP-OFGB bars andtheir application in reinforced concrete beamsrdquo in Proceedingsof the 1st International Conference on Structural Health Moni-toring and Intelligent Structure vol 13ndash15 pp 861ndash866 TokyoJapan November 2003

[12] HTsutsui AKawamata T Sanda andNTakeda ldquoDetection ofimpact damage of stiffened composite panels using embeddedsmall-diameter optical fibersrdquo Smart Materials and Structuresvol 13 no 6 pp 1284ndash1290 2004

[13] C-Y Ryu J-R Lee C-G Kim and C-S Hong ldquoBucklingbehaviormonitoring of a compositewing boxusingmultiplexedandmulti-channeled built-in fiber Bragg grating strain sensorsrdquoNDT amp E International vol 41 no 7 pp 534ndash543 2008

[14] S-I Takeda Y Aoki and Y Nagao ldquoDamage monitoringof CFRP stiffened panels under compressive load using FBGsensorsrdquo Composite Structures vol 94 no 3 pp 813ndash819 2012


[15] K I Tserpes V Karachalios I Giannopoulos V Prentzias andR Ruzek ldquoStrain and damage monitoring in CFRP fuselagepanels using fiber Bragg grating sensors Part I design man-ufacturing and impact testingrdquo Composite Structures vol 107pp 726ndash736 2014

[16] T C Triantafillou ldquoShear strengthening of reinforced concretebeams using epoxy-bonded FRP compositesrdquo ACI StructuralJournal vol 95 no 2 pp 107ndash115 1998

International Journal of

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Control Scienceand Engineering

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



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Civil EngineeringAdvances in

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Advances inOptoElectronics


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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation



DistributedSensor Networks



Secondly the FBG sensors are firstly clamped with the endedmechanical anchorage and then packaged by the additionalprotection It is inevitable that the creep of OFBG sensorswould occur under sustained loads due tomechanical clamp-ing therefore the measurement scale is just as the ultimatestrain of the FBG sensor In addition to this the durabilityis restricted by the material of the clamping devices Thirdlyadvanced composites can be introduced as packagingmateri-als such as fiber-reinforced polymer (FRP) including carbonfiber-reinforced polymer (CFRP) aramid fiber-reinforcedpolymer (AFRP) basalt fiber-reinforced polymer (BFRP)and glass fiber-reinforced polymer (GFRP) FRP compositesare originated from the design of large high-performancestructures in the aerospace industry A fundamental issuein the implementation of an OFBG-based SHM system incomposite structures aerospace area is the embedment ofsensors during manufacturing Tsutsui et al applied small-diameter optical fiber sensors to stiffened composite panelsfor the detection of impact damage [12] Ryu et al haveused multiplexed and multichanneled built-in FBG sensorsto monitor the buckling behavior of a composite wing box[13] Takeda et al used FBG sensors to monitor damage dueto compressive load in CFRP stiffened panels [14] Tserpeset al developed an integrated methodology for monitoringstrain and damage in CFRP fuselage panels and embedmentof fiber sensors in the panel during manufacturing was doneso as tominimize risk of fiber breaking duringmanufacturingand impact testing and to effectively capture strains beingrepresentative of the damage developed in the panel [15]

In this paper the bonding mechanism of the combi-nation of FRP and FBG sensors is explored firstly Andthen an experiment program is conducted for investigatingthe durability properties of BFRP bars and GFRP barswhich are used as typical encapsulation materials Thirdlyseries of FRP-packaged FBG strain sensors are developed forinfrastructures under harsh environment and their sensingperformance under normal environment and harsh envi-ronment is experimentally investigated Finally the practicalapplication of these FRP-packaged FBG strain sensors inAizhai Bridge SHM system is briefly introduced

2 Bonding Mechanism betweenFRP and FBG Sensors

As we know the sensing properties of FRP-packaged opticalfiber strain sensors are determined by the FBG and packagingmaterials Due to the small proportion of FBG the basicsensing performance properties such as linearity repeatabil-ity and measurement scale and the main durability indexare directly influenced by the basic mechanical and chemicalproperties of packaging materials Fiber-reinforced polymercomposites provide a reliable means for the developmentof high-performance packaged optical fiber strain sensorsowing to their linear-elastic material constitutive propertiesnamely the notion that the elastic modulus remains con-stant until failure (as shown in Figure 1) excellent fatigueperformance and durability Particularly for that the whole-process pseudoelasticity of FRP composites ensures the per-fect linearity and repeatability of the FRP-packaged optical

CFRP1CFRP2

CFRP-OFBG1CFRP-OFBG2

Strain (120583120576)5000450040003500300025002000150010005000

0

100

200

300

400

500

600

700

Stre

ss (M

Pa)

Figure 1 The constitutive curve of CFRP bar

fiber strain sensors in the whole measurement scale Thefundamental basis of taking FRP composites as packagingmaterials is further explained as follows

21 The Compatibility between FBG and FRP CompositesFrom the point of view of material component fiber-reinforced polymer composites commonly consist of glassfibers (or carbon fibers aramid fibers basalt fiber andhybrid fiber) resins additives and so forth Silica as thebasic composition of the optical fiber is also the mainmaterial composition of glass fibers Thus the glass fibers areinfiltrated in the resin and cure for molding easily which isthe same as optical fibers It is shown from the SEM photo(Figure 2) of bare FBG and FRP that the bare fiber FRPcombined well with FRP composites and worked together inthe manner of full interaction

22 Effect of FRP on the SensingCharacteristics of FBGSensorsThe main indexes of sensing elements are highlighted inlinearity measurement range repeatability and so forth andthe macroscopic constitutive property of FRP materials isjust linear elastic which ensures that the excellent linearityof the FBG sensor would be maintained after encapsulatingIn addition to that the FBG is precompressed and inducedby the shrinkage of the resin in the curing process ofthermosetting FRP composites due to their perfect bondingwith FRP composites and the precompressed section willbe the extended portion for the tensile strain measurementrange compared with the bare FBG sensor under the initiallyunstressed state According to the experiment results shownin Figure 3 the range of GFRP-packaged FBG sensor canreach up to 7000sim8000120583120576 By contrast the range of bareFBG sensors is only 3000sim4000 120583120576 Thus it can be seen thatFRP composites increase the measurement scale significantlywithout changing the sensing performance of the FBG sensor(Figure 5)




Protecting layer

Optical fiber

Adhesive layer

Host materials

o

2Lf

raprh

rc x

(a)

Protecting layer

Optical fiber

Adhesive layer

Host materials

uh(x)

uc(x)

Δa(x)

Δp(x)

(b)




119906 (119909) =


(1)


119906119888 (119909) = 119906119901 (119903119888 119909)119906119901 (119903119888 119909) = 119906119886 (119903119888 119909)119906119886 (119903119888 119909) = 119906ℎ (119909)

(2)

119906ℎ (119909) minus 119906119888 (119909) = Δ 119886 (119909) + Δ119901 (119909) (3)

119906119886 (119903ℎ 119909) minus 119906119886 (119903119886119901 119909) = Δ 119886 (119909) (4)

119906119901 (119903119886119901 119909) minus 119906119901 (119903119888 119909) = Δ119901 (119909) (5)

When 119909 = 0120576119888 (119903 0) = 120576119886 (119903 0) = 120576119886119901 (119903 0) = 120576ℎ (119903 0) (6)


sum119865119909 = 0 (7)

119889120590119888 (119909)119889119909 = minus2120591119901119888 (119903119888 119909)119903119888 (8)

119889120590119901 (119909)119889119909 = 2 [120591119901119888 (119903119888 119909) 119903119888 minus 120591119886119901 (119903119886119901 119909) 119903119886119901]1199032119886119901 minus 1199032119888 (9)

119889120590119886 (119909)119889119909 = 2 [120591119886119901 (119903119886119901 119909) 119903119888 minus 120591ℎ (119903ℎ 119909) 119903ℎ]1199032ℎminus 1199032119886119901 (10)


120591 (119903 119909) = 119903119886119901119903 120591119886119901 (119903119886119901 119909) 119903119888 le 119903 le 119903119886119901120591 (119903 119909) = 119903ℎ119903 120591ℎ (119903ℎ 119909) 119903119886119901 le 119903 le 119903ℎ

(11)

When 119903 = 119903119888 and 119903 = 119903119886119901119889120590119901 (119909)119889119909 = 0119889120590119886 (119909)119889119909 = 0

(12)

Therefore

120590119901 (119909) = cons tan 119905120590119886 (119909) = cons tan 119905 (13)


120576ℎ (119909) = 120590ℎ (119909)119864ℎ120576119888 (119909) = 120590119888 (119909)119864119888

120574119886 (119903 119909) = 120591 (119903 119909)119866119886 119903119886119901 le 119903 le 119903ℎ120574119901 (119903 119909) = 120591 (119903 119909)119866119901 119903119888 le 119903 le 119903119886119901

(14)


r

120590c(x)120591pc(rc x)

120591pc(rc x)

120590c(x) + d120590c(x)

x

rc

dx

(a) FBG

r

120590p(x)

120590p(x)

120591ap(rap x) 120590p(x) + d120590p(x)

xrcrap

120591pc(rpc x)120590p(x) + d120590p(x)

120591ap(rap x)


120591ap(rap x)

r

120590a(x)

120590a(x)

120591pc(rpc x)120590a(x) + d120590a(x)

xrhrap

120591ap(rap x)

120590a(x) + d120590a(x)

120591pc(rpc x)

dx

(c) Adhesive layer


Strain (120583120576)

LoadingUnloading

80006000400020000

0006

0004

0002

0000

Δ120582

120582


LoadingUnloading

0006

0004

0002

0000

Δ120582

120582

2000 4000 6000 80000

Strain (120583120576)




Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)


int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)


1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)


120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)


119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)


119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)


119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)


120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]


(28)



12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)





BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Protecting layer

Optical fiber

Adhesive layer

Host materials

o

2Lf

raprh

rc x

(a)

Protecting layer

Optical fiber

Adhesive layer

Host materials

uh(x)

uc(x)

Δa(x)

Δp(x)

(b)




119906 (119909) =


(1)


119906119888 (119909) = 119906119901 (119903119888 119909)119906119901 (119903119888 119909) = 119906119886 (119903119888 119909)119906119886 (119903119888 119909) = 119906ℎ (119909)

(2)

119906ℎ (119909) minus 119906119888 (119909) = Δ 119886 (119909) + Δ119901 (119909) (3)

119906119886 (119903ℎ 119909) minus 119906119886 (119903119886119901 119909) = Δ 119886 (119909) (4)

119906119901 (119903119886119901 119909) minus 119906119901 (119903119888 119909) = Δ119901 (119909) (5)

When 119909 = 0120576119888 (119903 0) = 120576119886 (119903 0) = 120576119886119901 (119903 0) = 120576ℎ (119903 0) (6)


sum119865119909 = 0 (7)

119889120590119888 (119909)119889119909 = minus2120591119901119888 (119903119888 119909)119903119888 (8)

119889120590119901 (119909)119889119909 = 2 [120591119901119888 (119903119888 119909) 119903119888 minus 120591119886119901 (119903119886119901 119909) 119903119886119901]1199032119886119901 minus 1199032119888 (9)

119889120590119886 (119909)119889119909 = 2 [120591119886119901 (119903119886119901 119909) 119903119888 minus 120591ℎ (119903ℎ 119909) 119903ℎ]1199032ℎminus 1199032119886119901 (10)


120591 (119903 119909) = 119903119886119901119903 120591119886119901 (119903119886119901 119909) 119903119888 le 119903 le 119903119886119901120591 (119903 119909) = 119903ℎ119903 120591ℎ (119903ℎ 119909) 119903119886119901 le 119903 le 119903ℎ

(11)

When 119903 = 119903119888 and 119903 = 119903119886119901119889120590119901 (119909)119889119909 = 0119889120590119886 (119909)119889119909 = 0

(12)

Therefore

120590119901 (119909) = cons tan 119905120590119886 (119909) = cons tan 119905 (13)


120576ℎ (119909) = 120590ℎ (119909)119864ℎ120576119888 (119909) = 120590119888 (119909)119864119888

120574119886 (119903 119909) = 120591 (119903 119909)119866119886 119903119886119901 le 119903 le 119903ℎ120574119901 (119903 119909) = 120591 (119903 119909)119866119901 119903119888 le 119903 le 119903119886119901

(14)


r

120590c(x)120591pc(rc x)

120591pc(rc x)

120590c(x) + d120590c(x)

x

rc

dx

(a) FBG

r

120590p(x)

120590p(x)

120591ap(rap x) 120590p(x) + d120590p(x)

xrcrap

120591pc(rpc x)120590p(x) + d120590p(x)

120591ap(rap x)


120591ap(rap x)

r

120590a(x)

120590a(x)

120591pc(rpc x)120590a(x) + d120590a(x)

xrhrap

120591ap(rap x)

120590a(x) + d120590a(x)

120591pc(rpc x)

dx

(c) Adhesive layer


Strain (120583120576)

LoadingUnloading

80006000400020000

0006

0004

0002

0000

Δ120582

120582


LoadingUnloading

0006

0004

0002

0000

Δ120582

120582

2000 4000 6000 80000

Strain (120583120576)




Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)


int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)


1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)


120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)


119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)


119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)


119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)


120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]


(28)



12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)





BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119906 (119909) =


(1)


119906119888 (119909) = 119906119901 (119903119888 119909)119906119901 (119903119888 119909) = 119906119886 (119903119888 119909)119906119886 (119903119888 119909) = 119906ℎ (119909)

(2)

119906ℎ (119909) minus 119906119888 (119909) = Δ 119886 (119909) + Δ119901 (119909) (3)

119906119886 (119903ℎ 119909) minus 119906119886 (119903119886119901 119909) = Δ 119886 (119909) (4)

119906119901 (119903119886119901 119909) minus 119906119901 (119903119888 119909) = Δ119901 (119909) (5)

When 119909 = 0120576119888 (119903 0) = 120576119886 (119903 0) = 120576119886119901 (119903 0) = 120576ℎ (119903 0) (6)


sum119865119909 = 0 (7)

119889120590119888 (119909)119889119909 = minus2120591119901119888 (119903119888 119909)119903119888 (8)

119889120590119901 (119909)119889119909 = 2 [120591119901119888 (119903119888 119909) 119903119888 minus 120591119886119901 (119903119886119901 119909) 119903119886119901]1199032119886119901 minus 1199032119888 (9)

119889120590119886 (119909)119889119909 = 2 [120591119886119901 (119903119886119901 119909) 119903119888 minus 120591ℎ (119903ℎ 119909) 119903ℎ]1199032ℎminus 1199032119886119901 (10)


120591 (119903 119909) = 119903119886119901119903 120591119886119901 (119903119886119901 119909) 119903119888 le 119903 le 119903119886119901120591 (119903 119909) = 119903ℎ119903 120591ℎ (119903ℎ 119909) 119903119886119901 le 119903 le 119903ℎ

(11)

When 119903 = 119903119888 and 119903 = 119903119886119901119889120590119901 (119909)119889119909 = 0119889120590119886 (119909)119889119909 = 0

(12)

Therefore

120590119901 (119909) = cons tan 119905120590119886 (119909) = cons tan 119905 (13)


120576ℎ (119909) = 120590ℎ (119909)119864ℎ120576119888 (119909) = 120590119888 (119909)119864119888

120574119886 (119903 119909) = 120591 (119903 119909)119866119886 119903119886119901 le 119903 le 119903ℎ120574119901 (119903 119909) = 120591 (119903 119909)119866119901 119903119888 le 119903 le 119903119886119901

(14)


r

120590c(x)120591pc(rc x)

120591pc(rc x)

120590c(x) + d120590c(x)

x

rc

dx

(a) FBG

r

120590p(x)

120590p(x)

120591ap(rap x) 120590p(x) + d120590p(x)

xrcrap

120591pc(rpc x)120590p(x) + d120590p(x)

120591ap(rap x)


120591ap(rap x)

r

120590a(x)

120590a(x)

120591pc(rpc x)120590a(x) + d120590a(x)

xrhrap

120591ap(rap x)

120590a(x) + d120590a(x)

120591pc(rpc x)

dx

(c) Adhesive layer


Strain (120583120576)

LoadingUnloading

80006000400020000

0006

0004

0002

0000

Δ120582

120582


LoadingUnloading

0006

0004

0002

0000

Δ120582

120582

2000 4000 6000 80000

Strain (120583120576)




Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)


int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)


1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)


120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)


119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)


119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)


119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)


120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]


(28)



12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)





BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










r

120590c(x)120591pc(rc x)

120591pc(rc x)

120590c(x) + d120590c(x)

x

rc

dx

(a) FBG

r

120590p(x)

120590p(x)

120591ap(rap x) 120590p(x) + d120590p(x)

xrcrap

120591pc(rpc x)120590p(x) + d120590p(x)

120591ap(rap x)


120591ap(rap x)

r

120590a(x)

120590a(x)

120591pc(rpc x)120590a(x) + d120590a(x)

xrhrap

120591ap(rap x)

120590a(x) + d120590a(x)

120591pc(rpc x)

dx

(c) Adhesive layer


Strain (120583120576)

LoadingUnloading

80006000400020000

0006

0004

0002

0000

Δ120582

120582


LoadingUnloading

0006

0004

0002

0000

Δ120582

120582

2000 4000 6000 80000

Strain (120583120576)




Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)


int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)


1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)


120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)


119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)


119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)


119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)


120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]


(28)



12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)





BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Therefore

119906ℎ (119909) = int1199090120576ℎ (119909) 119889119909 = int119909

0

120590ℎ (119909)119864ℎ 119889119909119906119888 (119909) = int119909

0120576119888 (119909) 119889119909 = int119909

0

120590119888 (119909)119864119888 119889119909Δ 119886 (119909) = int119903ℎ

119903119886119901

120574119886 (119903 119909) 119889119903 = 1119866119886 int119903ℎ

119903119886119901

120591119886 (119903 119909) 119889119903Δ119901 (119909) = int119903119886119901

119903119888

120574119901 (119903 119909) 119889119903 = 1119866119886 int119903119886119901

119903119888

120591119886 (119903 119909) 119889119903

(15)


int1199090

120590ℎ (119909)119864ℎ 119889119909= 119903119886119901120591119886119901 (119903119886119901 119909) [ 1119866119886 ln

119903ℎ119903119886119901 +1119866119901 ln

119903119886119901119903119888 ]

+ int1199090

120590119888 (119909)119864119888 119889119909

(16)

120590ℎ (119909)119864ℎ = 119903119886119901 [ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

120597120591119886119901 (119903119886119901 119909)120597119909+ 120590119888 (119909)119864119888

(17)

[ 1119866119886 ln119903ℎ119903119886119901 +

1119866119901 ln119903119886119901119903119888 ]

1205971205912119886119901 (119903119886119901 119909)1205972119909minus 21198641198881199032119888 120591119886119901 (119903119886119901 119909) = 0

(18)

where

12058221 = 21198641198881199032119888 [(1119866119886) ln (119903ℎ119903119886119901) + (1119866119901) ln (119903119886119901119903119888)] (19)


1205971205912119886119901 (119903119886119901 119909)1205972119909 minus 12058221120591119886119901 (119903119886119901 119909) = 0 (20)


120591119886119901 (119903119886119901 119909) = 119860 cosh (1205821119909) + 119861 sinh (1205821119909) (21)


119873119888 (119909) = int119860120590119888 (119909) 119889119909 (22)

noting that 120590119888(0) = 120590119888

And then

120590119888 (119909) = 120590119888 minus 21199031198861199011199032119888 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (23)

Therefore

119873119888 (119909) = 1205871199032119888120590119888 minus 2120587119903119886119901 int1199090120591119886119901 (119903119886119901 119909) 119889119909 (24)


119873119888 (119909) = 1205871199032119888120590119888minus 2120587119903119886119901 1120582 [119860 sh (120582119909) + 119861 ch (120582119909) + 119861] (25)


119873119888 (0) = 120590ℎ1205871199032119888 119864119888119864ℎ119873119888 (119897119891) = 0

119860 = 12059011988811990321198881205822119903119886119901sh (120582119897119891) 119861 = 0

(26)


120591119886119901 (119903119886119901 119909) = 12059011988811990321198881205822119903119886119901sh (120582119897119891)ch (120582119897119891) (27)

120576119888 (119909) = 120576119888 (0) times [1 minus sh (120582119909)sh (120582119897119891)]


(28)



12058221 = 2119866FRP1198641198881199032119888 ln (119903ℎ119903119888) (29)





BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












BFRP






GFRP







120576119888 (119909) = int1198971198910120576119888 (119909) 119889119909119871119891

120576ℎ (119909) = int1198971198910120576ℎ (119909) 119889119909119871119891


119896 = 11 minus 120578

(30)








BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

250200150100500600

700

800

900

1000

1100Te

nsile

stre

ngth

(MPa

)

Corrosive time (d)

(a)

250200150100500minus50

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

Tens

ile st

reng

th ch

ange

rate

()

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)


250200150100500

47

48

49

50

51

52

53

54

Tens

ile m

odul

us (G

Pa)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

250200150100500minus8

minus6

minus4

minus2

0

2

4

6

8

10

Mod

ulus

chan

ge ra

te (

)

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(b)







30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










30

35

40

45

50

Inte

rlam

inar

shea

r stre

ngth

(MPa

)

250200150100500

BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

Corrosive time (d)

(a)

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

The c

hang

e rat

e of i

nter

lam

inar

shea

r stre

ngth

()


BFRP-saltGFRP-salt

BFRP-acidGFRP-acid

(b)



















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















Strain (120583120576)

0000

0002

0004

0006

Δ120582

120582

80006000400020000

LoadingUnloading


LoadingUnloading

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500300015000


Strain (120583120576)4500300015000

LoadingUnloading

0000

0001

0002

0003

0004

Δ120582

120582


0005

0004

0003

0002

0001

0000

Δ120582

120582

Strain (120583120576)4500 6000300015000

LoadingUnloading


Strain (120583120576)

Fitting

3000200010000

0000

0001

0002

Δ120582

120582

Circle 1Circle 2

Circle 3


Strain (120583120576)

Circle 1Circle 2

Circle 3Fitting

20000 60004000

0000

0002

0004

0006

Δ120582

120582





















Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



























Strain (120583120576)



Δ120582 = 1537703 + 000113 lowast 120576R = 099976

14001300120011001000900800700600500

15383

15384

15385

15386

15387

15388

15389

15390

15391

15392

15393W

avele

ngth

(120583m

)

(a) 20∘C



Strain (120583120576)

Δ120582 = 1538456 + 00017 lowast 120576

R = 099987

2200180014001000600200

15385

15390

15395

15400

14505

15410

Wav

eleng

th (120583

m)

(b) 60∘C



Strain (120583120576)

Δ120582 = 1539097 + 000119 lowast 120576

R = 099966

25002000150010005000

15390

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

(c) 80∘C



Strain (120583120576)

Δ120582 = 1539505 + 000113 lowast 120576

R = 099969

15394

15396

15398

15400

15402

15404

15406

15408

15410

15412

15414W

avele

ngth

(120583m

)

180014001000600200minus200

(d) 100∘C



Strain (120583120576)

R = 099982

15395

15400

15405

15410

15415

15420

Wav

eleng

th (120583

m)

Δ120582 = 1539855 minus 00011 lowast 120576

180014001000600200minus200

(e) 120∘C



Strain (120583120576)

R = 099954

120010008006004002000

15402

15404

15406

15408

15410

15412

15414

15416

Wav

eleng

th (120583

m)

Δ120582 = 1540243 + 000103 lowast 120576

(f) 140∘C













6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















6 Conclusions




Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Time (s)Measurement

11500438572

11500438571

11500438570

11500438569

11500438568

15805

15810

15815

15820

15825

15830W

avele

ngth

(nm

)

(a) 2247

Time (s)Measurement

11509499430

11509499429

11509499428

11509499427

11509499426

15625

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(b) 028

Measurement

11509581595

11509581596

11509581597

11509581598

11509581599

Time (s)

15620

15615

15610

15605

15600

Wav

eleng

th (n

m)

(c) 245Measurement

Time (s)

11500643778

11500643779

11500643780

11500643781

11500643782

15610

15615

15620

15625

15630

15635W

avele

ngth

(nm

)

(d) 429

Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509722794

11509722795

11509722796

11509722797

11509722798

Time (s)

(e) 640Measurement

15635

15630

15625

15620

15615

15610

Wav

eleng

th (n

m)

11509764373

11509764374

11509764375

11509764376

11509764377

Time (s)

(f) 753




Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Δ120582 = 124120576

R = 099999

0

500

1000

1500

2000

2500

3000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 2000 25000

Strain (120583120576)

(a)

Δ120582 = 109120576

R = 099976


500 1000 1500 20000

Strain (120583120576)

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)(b)


Δ120582 = 103120576R = 099954

0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)


(c)


Δ120582 = 1022120576

R = 099958


0

500

1000

1500

2000

Wav

eleng

th ch

ange

(pm

)

500 1000 1500 20000

Strain (120583120576)

(d)





Competing Interests




121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











121

3000

56800


Main-tower strain





Cable tension force

Main-beam strain


Main-beam strain


Cable tension force

Main-beam vibration


Main-beam strain




Cable tension force

Main-beam vibration


Main-beam strain


Main-beam strain



Main-tower strain




References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Fiber-Reinforced Polymer-Packaged Optical...

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