STRUCTURAL OPTIMIZATION AND PROPOSITION OF PRE-SIZING ... · cia em Projeto” (translation:...

STRUCTURAL OPTIMIZATION AND PROPOSITION OFPRE-SIZING PARAMETERS FOR UAVS WING SPARS

Fernanda Amorim Fenelon∗ , Geovana Neves Felix Silva∗ , Rodrigo de Sá Martins∗∗Universidade Federal de Minas Gerais

Keywords: UAV, structural optimization, spar, genetic algorithm, pre-sizing

Abstract

UAVs are a growing segment in the aviation mar-ket and it has arisen the necessity of lighter andlow cost design. Considering this, the presentwork’s goal is to propose an optimized pre-sizingof an UAV wing spar using genetic algorithm op-timization method followed by a finite elementsanalysis, which also provides low computationalcost.

1 Introduction

Nowadays the unmanned aerial vehicles (UAVs)are responsible for the expansion of aerospaceindustry representing a growing segment of theaviation market. In this scenario, it is necessarylighter and low cost design to reduce the UAVsoperational cost promoting their use and produc-tion not only in the universities but also in theindustry.

This can be done by applying optimizationtechniques considering the suitable ones for eachstage of the design process. The paper focus onthe preliminary phase of the UAV wing structuraldesign [1]. The methodology developed is basedon the approximation concept discussed by [2]for a single-discipline optimization.

The methodology proposed was applied inthe aircraft Mach Crítico designed at CEA (Cen-tro de Estudos Aeronáuticos) - UFMG (Univer-sidade Federal de Minas Gerais). The UAVcompeted in the the Regular Class of the SAEAERODESIGN BRASIL Competition 2017 (So-ciety of Automotive Engineers). In this con-

text, the aircraft must meet geometric restrictionsand must not have a MTOW (Maximum TakeoffWeight) greater than 20kg [3]. Also, the projectis evaluated through a score system, which is cal-culated based on the maximum payload and onthe engineering solutions developed by the un-dergraduate students. The structural design mustbe the lightest possible to minimize the aircraftempty weight. In addition, the structure must bedesigned in a short time and with low-cost meth-ods. This scenario is very similar to the currentUAV industry and the methodology developed atCEA for the wing spar design is useful for similaraircrafts.

The Mach Crítico aircraft presented in Fig-ure 1 received the "Troféu Embraer de Excelên-cia em Projeto” (translation: Embraer Trophyof Design Excellence) by Embraer S.A. and theAward of Structure Optimization by Altair Engi-neering. These achievements show that the sim-ple methodology developed for structural designgives satisfactory results for this type of aircraft.

Fig. 1 Mach Crítico UAV

The methodology is mainly divided in threeparts: optimized pre-sizing, FEM analysis andcompliance with aeroelastic criterion. Section

1

F. A. FENELON , G. F. S. NEVES , R. S. MARTINS

2.1 presents the first part, section 2.2 describesthe second, and 2.3 presents the final one. Section3 shows and discusses the results obtained for theMach Crítico UAV. Sections 4 and 5 point outthe results achieved and possible improvementsin the methodology.

2 Methodology

2.1 Optimized structural pre-sizing

2.1.1 Structure Modeling

The wing structure must resist to all externalloads and the most significant ones are the liftforce and the aerodynamic moment for lightUAV. The loads were previously calculated con-sidering methodology suggested by Iscold [4]and Neves [5] which models the airplane as arigid body. In the present work, the semi-wingspar is modeled as a cantilever beam and as a can-tilever torsion shaft once it has been idealized asthe structure supposed to resist to all loads. Thisdecision was made to increase the wing struc-tural efficiency. The final semi-spar is presentedin Figure 2.

Fig. 2 Final semispar.

According to Niu [6], the section methodis used to compute the internal loads, such asshear force, bending moment and torsion mo-ment along the semi-span. The beam is sec-tioned off at multiple desired coordinates alongthe semi-span and the equilibrium equations areapplied to the sectioned structure. The unknownvariables will be the internal loads since the ex-ternal loads are previously known. The shearforce and bending moment due to aerodynamicloads can be determined regardless the shear cen-ter position. However, once the spar position

along the chord is one of the optimization param-eters for each section optimized, the resulting ap-plied torsion moment at the shear center (whichis a function of the spar position) has to be calcu-lated during the optimization process, as shownbelow. In this work, the shear center was approx-imated as the cross-section center.

dT = dM+δdL (1)

dT - applied torsion moment at the section of in-terest at the shear center;

dM - aerodynamic moment at the section of in-terest at the aerodynamic center;

dL - lift force at the section of interest at theaerodynamic center;

δ - distance between the shear center and theaerodynamic center.

Moreover, since the torsion moment at theroot section depends on the torsion momentof the next sections, the optimization processstarts from the tip to avoid unknown parameters.Therefore, it calculates the ensuing section up tothe root using the known values of torsion mo-ment from the previous sections starting from thetip.

The direct stresses in each section due to in-ternal loads are determined according to Megson[7] using the Euler-Bernoulli Beam Theory as ex-pressed by Equation 2.

σyy = Ez,i ·Mx · (I′zz · z− I′xz · x)

I′xx · I′zz− Ixz′2(2)

σyy - tension or compression stress;Ez,i - laminate elasticity modulus;Mx - bending moment;I′xx =

∫Ez,i · z2dA- modified second moment of

area about x axis;I′zz =

∫Ez,i · x2dA- modified second moment of

area about z axis;I′xz =

∫Ez,i · x · zdA - modified second moment of

area about the axis perpendicular to x andz axes;

x - x coordinate (from the centroid);z - z coordinate (from the centroid).

2

STRUCTURAL OPTIMIZATION AND PROPOSITION OF PRE-SIZING PARAMETERS FOR UAVsWING SPARS

In this work, every ply of laminate is directedwith a 0◦angle ply which means Ez,i is constantalong the cross-section area. This simplifies thelatter equation to the Equation 3.

σyy =Mx · (Izz · z− Ixz · x)

Ixx · Izz− Ixz2 (3)

σyy - tension or compression stress;Mx - bending moment;Ixx =

∫z2dA- second moment of area about x

axis;Izz =

∫x2dA- second moment of area about z

axis;Ixz =

∫x · zdA - second moment of area about the

axis perpendicular to x and z axes;x - x coordinate (from the centroid);z - z coordinate (from the centroid).

The maximum shear stress in the webs dueto the shear force in addition with the shear stresscaused by the torsion moment is calculated as ex-pressed in Equation 4. Here, it is already consid-ered that all plies in the laminate are directed witha 0◦angle ply.

τzy =Vz ·Qx−max

Ixx ·2 · tw+

T2 ·A · tw

(4)

τzy - shear stress;Vz - shear force;Qx−max - first moment of area about the cross-

section neutral axis;tw - web thickness;T - torsion moment;A - area enclosed by the median contour.

The angles of twist are calculated, accord-ing to Megson [7], during the pre-sizing with theBredt’s Formula presented in Equation 5 alreadysimplified for all plies in the laminate directedwith a 0◦angle ply.

dθ

dy=

12 ·A ·G

∫ qt

ds (5)

s - coordinate along the contour;y - coordinate along the span;G - material’s shear modulus;A - area enclosed by the section median contour;

t - wall thickness;T - torsion moment;q = T

2·A - shear flow;θ - angle of twist.

Then, the stresses are compared with the al-lowable stresses of the material considering ulti-mate loads in order to determine either the struc-ture is safe or not. Also, the angle of twist is com-pared to the allowable angle of twist as shown insection 2.1.3.

2.1.2 Parameterization and Strategies

As discussed earlier, the problem is to optimizethe whole wing spar, so it consists of determiningthe materials used and the structure’s dimensionsalong the span.

First, the wing spar materials play an impor-tant role in the spar design so it has to be decidedwhich materials will be analyzed and their me-chanical properties have to be known. The wingof Mach Crítico UAV has a complex geometryas shown in Figure 1. Therefore, in this case,the material chosen was carbon fiber laminate inorder to meet aerodynamic requirements. Eventhough the results presented here are for carbonfiber laminate, the method presented can be eas-ily adapted to other materials. The mechanicalproperties of the carbon fiber laminate were de-termined at CEA-UFMG via tensile, compres-sion and shear tests according to ASTM D3039,ASTM D6641, and ASTM D7078. The PVCfoam mechanical properties were determined bythe foam manufacturer. All properties are pre-sented in tables 1 and 2.

PVC foam mechanical properties

Limit stress:Tension [MPa] 1.8

Compression [MPa] 0.9Shear [MPa] 0.78

E [MPa] 72

G [MPa] 21

Density [kg/m3] 60

Table 1 PVC foam mechanical properties.

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Bidirectional carbon fiber mechanical propertiesParallel Perpendicular

Limit stress:Tension [MPa] 682 682

Compression [MPa] 341 341Shear [MPa] 72 72

E [MPa] 51000 48929

G [MPa] 2000 1980

ν 0.28 0.02

Density [kg/m3] 1545 1545

Table 2 Bidirectional carbon fiber mechanicalproperties.

The second step is to brake the problem intoa finite number of spar sections along the wingsemi-span. For the Mach Crítico UAV, the wingsemi-span is 1.30m and it was devided into 21sections (Figure 3) in order to meet both manu-facturing requirements and the structural theoryhypothesis.

Fig. 3 Wing spar sections for the Mach Crítico UAV

With both material and number of sectionsdefined, the next step is to choose which beamcross-sections will be analyzed. In order to resisttorsion efficiently, the beam cross-section neededto be a closed one. Therefore, the beam cross-sections proposed and theirs suggested parame-terization are presented in Figure 4 and Figure 5.

Fig. 4 Suggested cross-section 1

Number of parameters: 6

pw1 - position of the first web;w - width of the spar;o f f set - space between the upper camber and

the upper cap;tw - web thickness;tc - upper cap thickness;tt - lower cap thickness.

The o f f set was introduced because of manu-facturing methods used to guarantee the aerody-namic profile.

Fig. 5 Suggested cross-section 2

Number of parameters: 2

pw - position of the web;t - spar thickness.

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2.1.3 The Optimization Problem

The optimization problem is to minimize theweight of the spar:

minimizex

Wspar(x)

subject to bli ≤ xi ≤ bui, i = 1, . . . ,m.(6)

Wspar - spar weight i;xi - design variable i (See figures 4 and 5);m - number of design variable;bli - lower bound for xi;bui - upper bound for xi.

This is a single-objective optimization andit is structured to be with no constraints sincepenalties are applied to the objective functionwhen the structure is not suitable. Also, someof the design variables are discrete since theirvalues depend on the number of carbon fiberplies, for example, the wall’s thickness is amultiple of the thickness of the ply. There-fore, the single-objective optimization is a mixeddiscrete/continuous problem, unconstrained andbounded since the design variables have upperand lower limits according to geometric restric-tions and manufacturing requirements. A geneticalgorithm (’DE/rand/1/bin’ [8]) was chosen dueto the nature of the optimization problem [9] andit was implemented using MATLAB.

One optimization is performed for each panelin order to have an optimization process witha low number of parameters. Considering theMach Crítico UAV, if the whole spar was opti-mized at once, the option presented in Figure 4would end up with 126 parameters and the onepresented in Figure 5, 42. These numbers of pa-rameters may lead to difficulties while solvingthe optimization problem since it has multiple lo-cal minimums. It is not guaranteed that the globalminimum is reached in a short time, however de-creasing the number of parameters, the optimiza-tion leads to results faster. Therefore, it was de-cided to perform an optimization for each panelusing the genetic algorithm since it is efficientand it can handle the characteristics of the opti-mization problem with the parameterization pro-

posed. Furthermore, the genetic algorithm is sim-ple to implement, to set up the optimization andit also can be easily parallelized. The goal withthis methodology is to obtain satisfactory resultswith low-cost and in less time.

The penalty strategy is applied in the objec-tive function. It calculates the mass of the panelwhose section is being optimized by estimatingits volume and multiplying it by the material’sdensity. Thus, the stresses are calculated andeach one is compared to its corresponding allow-able stress. If the allowable stress is greater thanthe calculated one there is no penalty applied tothe mass panel of the section tested in the op-timization. On the other hand, if the allowablestress is overcome by the calculated one, the masspanel of the section tested is multiplied by a fac-tor proportional to how much it fails by as illus-trated in equations 7 and 8. The constant wasiteratively defined in order to achieve the best op-timization solution.

The wing’s angle of twist is an important pa-rameter during the design process and one ofthe most efficient ways of reducing the angleof twist is to increase the spar’s closed sectionarea. In addition, according to Barros [10], thetotal angle of twist should not be greater than 4◦

when 62.5% of the maximum torsion moment isapplied. However, these 4◦ can be distributedalong the semi-span in very different ways. Foreach distribution, there is an optimum choice ofspar. Consequently, many distributions were gen-erated and the optimization process was testedwith them to identify which one of the distribu-tions fitted best in the problem analyzed (whichone resulted in the lighter spar).

For the Mach Crítico UAV, the best angle oftwist distribution found was the one representedby the black curve shown in Figure 6. This dis-tribution was adopted as the allowable angle oftwist. On each section the incremental value ofthe allowable angle of twist is compared to thecalculated one. If the calculated is greater thanthe allowable one, there is a penalty applied tothe tested section as shown in Equation 9. Themultiplying constant was chosen in order to ob-tain the lightest spar.

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M f inal = (Pstress +Ptwist angle) ·MEstimated (7)

Pstress =Cstress ·σ−σallowable

σallowable(8)

Ptwist angle =Ctwist angle ·∆θ−∆θallowable

∆θallowable(9)

M f inal - panel mass considered during optimiza-tion;

MEstimated - estimated panel mass;Pstress - penalty due to stress evaluation;σ - calculated stress;σallowable - allowable stress;Cstress - penalty constant of angle of twist;Ptwist angle - penalty due to twist angle evalua-

tion;∆θ - calculated panel angle of twist;∆θallowable - allowable panel angle of twist;Ctwist angle - penalty constant of angle of twist.

Fig. 6 Evaluated angle of twist distributions -Mach Crítico UAV

2.1.4 Post-Processing of the Pre-Sized Spar

As it was presented before, each section is pre-sized and positioned along the chord separatelywhich does not guarantee a manufacturable andsmooth spar. Therefore, it is necessary to an-alyze the first results and identify its tendency.

Then, another whole optimization process maybe performed with new upper and lower boundsfor spar position based on the analysis made. Thenew results shall be analyzed and new bounds de-fined for another optimization until the final andmanufacturable spar is defined. The spar positionalong the chord and its width deserve a specialattention when it comes to the adjustments to en-sure it is manufacturable. The Figure 7 shows thedifference between the adjusted spar width andthe optimized spar without modifications for theMach Crítico UAV.

Fig. 7 Comparison between adjusted spar widthand the optimized spar without modifications -Mach Crítico UAV

2.2 Buckling Analysis

It is known that the buckling problem is effi-ciently solved using a sandwich structure made ofcarbon fiber and PVC foam. However analyzingthis kind of structure during an optimization pro-cess would increase its computational and timecosts. These are the reasons why the spar buck-ling is supposed to be analyzed after the structureis pre-sized in order to reduce model complexity.

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The pre-sized structure was analyzed in Hy-perWorks, an Altair FEM software. It was mod-eled with the element CQUAD4 and the propertyPCOMP, the constraints were applied to the holesof the ribs which connect the wing to the fuse-lage using the rigid element RBE2 and restricting5 degrees of freedom. The ultimate loads wereapplied to the structure using the rigid elementRBE3.

2.3 Aeroelastic criterion

Also, modifications may be necessary in order tothe spar comply with aeroelastic criterion. Forlight UAV, it is suggested to use [11] as a require-ment since its application is simple and conserva-tive. The torsional flexibility of the wing shouldnot be greater than a constant which is functionof the dive speed [11]:

F =∫

θiC2i ds (10)

F ≤ 200V 2

D(11)

F - torsional flexibility of the wing;θi - angle of twist of the wing at station i, per unit

torsional moment applied at a wing stationoutboard of the end of the aileron ( rad

f tlb );Ci - wing chord length at station i ( f t);ds - increment of span ( f t);VD - Design dive speed (IAS) of the airplane.

An increase in the cross-section area of thespar may be made so the torsional stiffness of thewing is increased and the torsional flexibility de-creased.

3 Results

The final spar passed through three main process:the optimized pre-sizing, the FEM analysis andaeroelastic verification.

The optimized pre-sizing was performed fortwo kinds of beam cross-sections, as presentedbefore. The lightest one was the suggested cross-section 1 with half of the suggested cross-section2 mass. One of the reasons for this difference is

that the second type of cross-section had its tor-sional axis closer to the leading edge than the firstone, having to resist to a greater torsional mo-ment. The angle of twist was the most demand-ing characteristic in the optimization. The opti-mization process was continued for the section 1and after altering the parameter’s bounds and op-timizing 4 more times to meet manufacturing re-quirements, the final results of the pre-sized sparare shown in Figure 8.

Fig. 8 Results of pre-sizing optimization aftermanufacturing adjustments.

Position(m) - first web position measured rela-tively to the wing trailing edge;

θ (◦) - angle of twist;Width(m) - distance between the webs.

Second, the FEM analysis were performed.The Linear Static Analysis was performed usingthe Tsai Wu failure criteria and the structure didnot fail, as expected. Also, the Linear Buck-ling Analysis was performed revealing a severebuckling issue. The most critical regions werereinforced with a sandwich structure while oth-ers only needed another ply of carbon fiber. The

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adjustments added 92 g to the spar’s weight. Al-though the pre-sized thickness was altered, its po-sition along the chord and its geometric form wasmaintained. The final buckling eigenvalue of thespar was 1.025 for its ultimate load as shown inFigure 9. It was desired a small margin of safetyin buckling at this moment of the design becausethe Mach Crítico UAV wing had another carbonfiber laminate structure, the slat, which was notbeing considered initially. Later, another modelwas built for the whole wing and the bucklingFEM analysis showed that the spar final bucklingeigenvalue was 1.231.

Fig. 9 Buckling analysis results after the sparwas modified to meet the buckling requirement.

Third, the analysis of the aeroelastic criterion[11] showed that it was necessary to reduce thetorsional flexibility. This was done by augment-ing the spar width in some sections which added22 g. The modifications allowed the spar to re-sist a greater torsional moment. Thus, it was de-cided to change the spar position along the chordbringing it closer to the leading edge. This choicewas made because it would not add any weightto the structure and the torsional axis would bebetween the leading edge and the quarter chord,which is a desirable characteristic in the stand-point of aeroelasticity.

The design evolution during these processesare presented in the tables 3, 4 and 5 . The thick-ness is in number of carbon fiber plies of 0.25 mmeach, and S stands for sandwich which means thatthere is a sandwich of 4 mm thickness PVC foamand two carbon fiber plies of 0.25 mm thickness.The spar’s webs positions along the chord aremeasured relatively to the fourth of ninth rib sec-

tion chord for the first nine sections while the oth-ers are measured relatively to there own fourth ofchord, as shown in the Figure 10 below. All car-bon fiber plies are at 0◦angle.

Rib 1 4 7 8 12 16Station [mm] 35 320 600 693 1021 1294

pw1 [mm] 20 20 20 20 -5 -5w [mm] 42 40 34 28 12 7

Number of Carbon Fiber Pliestw 1 1 1 1 1 1tt 1 1 1 1 1 1tc 1 1 1 1 1 1

Table 3 After optimized pre-sizing - Mass of thespar: 125g

Rib 1 4 7 8 12 16Station [mm] 35 320 600 693 1021 1294

pw1 [mm] 20 20 20 20 -5 -5w [mm] 42 40 34 28 12 7

Number of Carbon Fiber Pliestw S 2 2 2 1 1tt 1 1 1 1 1 1tc S S 2 2 1 1

Table 4 After FEM Analysis - Mass of the spar:217g

Rib 1 4 7 8 12 16Station [mm] 35 320 600 693 1021 1294

pw1 [mm] -30 -30 -30 -30 -15 -15w [mm] 42 40 34 30 30 30

Number of Carbon Fiber Pliestw S 2 2 2 1 1tt 1 1 1 1 1 1tc S S 2 2 1 1

Table 5 After Aeroelastic Verification using [11]as criteria - Mass of the spar: 239g

pw1 - is the position of the first web measuredrelatively to the 1

4 of the reference chord;

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S - means that the section is a sandwich struc-ture composed by carbon fiber and foam.

Fig. 10 Coordinate system for the first web position.

4 Discussion

The design evolution began with the optimizedpre-sizing. In this phase the structural theoriesused were simple and the spar was pre-sized con-sidering direct and shear stresses and the angle oftwist. It was pre-sized and positioned along thechord and weighted 125g. After, in FEM analysisthe Tsai Wu failure criterion was checked and thebuckling problem was solved adding plies and asandwich structure where it was fit to. The mod-ifications added 92g. Then, the torsional flexibil-ity had to be reduced, as the analysis using theaeroelastic criterion in [11] showed, augmentingthe width of some sections. It added 22g. Also,the spar position was modified to reduce the dis-tance between the leading edge and the torsionalaxis with no addition in weight. The last change,not mentioned before, was in the manufactur-ing method and it added 61g. Every increase inweight was justified and some were expected be-fore hand.

As a way of verifying if the methodology pro-posed here was successful, its structure weightwas compared to another wing structure weightmade of composite materials and composed of aspar and a torsion box. Both aircrafts had similarMTOW’s. The other structure was 27% heavierthan the one presented here.

The design methodology presented here wassuitable for the Mach Crítico UAV. However,there are ways of improving it. Adding the an-gle of ply to the optimization parameters may

be profitable. Also, using a composite stresscriterion during the pre-sizing is a suggestion.New types of beam cross-sections may be pro-posed and evaluated. Also, other kinds of algo-rithms for optimization may be tested. It is alsorecommended to repeat the optimization processconsidering the approximation concept [2]. Inother words, after the modifications were made inthe pre-sized spar, another optimized pre-sizingshould be done with new bounds which considerthe modifications. An example of how the mod-ifications can feed the pre-sizing is the changein the spar position along the chord after thechanges were made.

5 Conclusion

The wing spar design presented here had the pur-pose to design a light structure for the UAV in ashort time. The methodology adopted had threemain phases. The first one was the spar opti-mized pre-sizing using a genetic algorithm im-plemented in MATLAB along with the Euler-Bernoulli Beam Theory. Then, the spar wasmodified to meet aeroelastic criterion. Finally,the spar was analyzed in a finite elements soft-ware and the buckling problems were solved us-ing a sandwich structure. The resulting struc-ture was satisfactory and the design process wasfast enough. The methodology developed hereachieved its goals. It can be adapted to otherUAVs designs and it can be improved as sug-gested before.

References

[1] Snorri Gudmundsson. General aviation air-craft design: Applied Methods and Procedures.Butterworth-Heinemann, 2013.

[2] Jaroslaw Sobieszczanski-Sobieski andRaphael T Haftka. Multidisciplinary aerospacedesign optimization: survey of recent devel-opments. Structural optimization, 14(1):1–23,1997.

[3] Sae aerodesign brasil 2017. http://portal.saebrasil.org.br/Portals/0/PE/AERODESIGN/AERO%202017/Regulamento_SAE_BRASIL_

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AeroDesign_2017_Rev00.pdf. Ac-cessed: 2017-07-26.

[4] Paulo H Iscold. Introducao as cargas nas aeron-aves. UFMG, 2002.

[5] Geovana F S Neves. Determinacao do dia-grama vn para vants a partir de simulacao de voocom 6 graus de liberdade. SAE AERODESIGNBRASIL, 2018.

[6] Michael C Y Niu. Airframe stress analysis andsizing. Hong Kong Conmlit Press Ltd, 1999.

[7] T H G Megson. Aircraft Structures for engi-neering students. Elsevier Ltd, 2012.

[8] Ferrante Neri and Ville Tirronen. Recent ad-vances in differential evolution: a survey andexperimental analysis. Artificial IntelligenceReview, 33(1-2):61–106, 2010.

[9] Garret N Vanderplaats. Numerical optimiza-tion techniques for engineering design, vander-plaats research & development. Inc., ColoradoSprings, CO, 1999.

[10] Claudio P Barros. Uma metodologia para o de-senvolvimento de projeto de aeronaves leves esubsônicas. Belo Horizonte, 2001.

[11] Robert Rosenbaum. Simplified flutter preven-tion criteria for personal type aircraft. Technicalreport, FEDERAL AVIATION ADMINISTRA-TION WASHINGTON DC, 1955.

Contact Author Email Address

• Fernanda Fenelon

[email protected]

• Geovana Neves

[email protected]

• Rodrigo de Sá Martins

[email protected]

Copyright Statement

The authors confirm that they, and/or their companyor organization, hold copyright on all of the origi-nal material included in this paper. The authors alsoconfirm that they have obtained permission, from thecopyright holder of any third party material includedin this paper, to publish it as part of their paper. The

authors confirm that they give permission, or have ob-tained permission from the copyright holder of thispaper, for the publication and distribution of this pa-per as part of the ICAS proceedings or as individualoff-prints from the proceedings.

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