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<0D-A130 346 AN EVALUATION OF VISCOELASTIC COATINGS AS LOW FREQUENCY 1//ACOUSTIC ABSORBERS(Ul DYNAMICS TECHNOLOGY INC TORRANCECA Y CHEN ET AL. MAY 83 DTN-8265-01 N00014-82-C-0769

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- Dynamics Technology, Inc.DTN-8256-01

AN EVALUATION OF

VISCOELASTIC COATINGS AS

LOW FREQUENCY ACOUSTIC ABSORBERS

May 1983

Ey: Y. M. Chen and R. L. Gran

Submitted to: Dr. E. Y. Harper

Office of the Chief of Naval Operations

OP-021T, 4D544

PENTAGONWashington, D.C. 20350

DTIPELEC- U

Dynamics Technology, Inc. JU I 3m022939 Hawthorne Blvd., Suite 200C) A

Torrance, California 90505,__ (213) 373-0666

88 07 08 064

This report has undergone an extensive internal review before

release, both for technical and non-technical content, by the

Division Manager and an independent internal review committee.

Division Manager:

Internal Re :ew:

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (Whon Dots Entered)

REPOT DCUMNTATON AGEREAD INSTRUCTIONSREPOT WUMETATON AGEBEFORE COMPLETING FORMIREPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

DTN-8265-01 L D-AI30 34/10 ____________

46. TITLE (and S.,bI,tie) S. TYPE OF REPORT II PERIOD COVERED

September 1982-AN EVALUATION OF VISCOELASTIC COATINGS AS FINAL May 1983LOW FREQUENCY ACOUSTIC ABSORBERSPEFRIGO.RPRTNMR

DTN-8265-017 AUTHOR(*) 9. CONTRACT OR GRANT NUMBER(,)

Yie-Ming Chen and Robert L. Gran N00014-82-C-0769

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

Dynamics Technology, Inc. AREA & WORK UNIT NUMBERS

22939 Hawthorne Blvd., Suite 200Torrance, CA 90505

II. CONTROLLING OFFICE NAME AND ADDRESS N004 2 REPORT DATE

Office of Naval Research N004May 1983Department of the Navy 13. NUMBER OF PAGES

800 N. Quincy, Arlington, VA 22217 6614 MONITORING AGENCY NAME AS ADDRESS(If different Ira,, ConitrollIngi Office) IS SECURITY CLASS. to# th, report)

Office of the Chief of Naval Operations UNCLASSIFIEDOP-021T, 4D544 PENTAGON_____________

Washigton D.CIS035 DECLASSI FICATION DOWNGRADING

Washington, D. . 20 5 SCHEDULE

16. DISTRIBUTION STATEMENT (of thii Rop.rrj

Unlimited

I7 DISTRIBUTION STATEMENT (of the *bstraet entered in Block JO, it different from Report)

Uni1 i ni ted

IS SUPPLEMENTARY NOTES

19 RI V WORD3S O',nI .... . ... .t . &*Ierr and td~fitI hr block -mflbe,)

anechoic coatingslow frequency acoustic absorbersviscoelastic dynamic propertiestarget strength reduction

2JABSTRACT ,nIn n .......e ado Of ,oreseerv and Idenitf by block noswborl

This study examines the effectiveness of elastomer coatings for specular,acoustic backscatter reduction in low frequency, under-water applications.Polybutadiene, and Thiokol RD. Their coating reflection loss for CW and

F impulse incident acoustic plane waves was examined using techniques andcomputer codes developed based on a geometric acoustics approach. The per-formance of these elastomer coatings was examined in the frequency range from10 Hz to 10 kHz, the pressure range 0 to 500 psig, and the temperature range.,

D ' po 1473 EDITION OF I NOYVSS IS OBSOLETE UNCLASSIFIED 4SECURITY CLASSIFICATION OF THIS PAGE t*%on Dote Ented

~~umgtUNCLASSIFIEDUIjTV CLASSIFICATION OF THIS PAGIE[lm Da eEnered)

00 to 30°C; ranges commonly encountered in oceanic applications. The resultsindicate that at low frequencies (order 100 Hz), the available elastomers,applied as homogeneous coatings up to 20 cm thick, are not sufficient toobtain reflection reduction greater than 6 dB for the specified conditions.Greater specular backscatter reduction may be achieved by using layered,inhomogeneous coatings, but a more relevant approach for these low frequen-cies may involve the examination of structural resonant response to theincident acoustic field since the body size and acoustic wavelength are ofthe same order of magnitude (Gaunard, 1977). The structural resonantmechanism of backscatter is probably dominant at low frequencies.

II

SI

UNCLASSIFIED12CUNITV CLASSIFICATION OF TwIS PAOGEt'Ien Date Entered)

u f Dynamics TechnologyDTN-8256-01

ACKNOWLEDGEMENTS

The technical monitor for this study is Dr. E.Y. Harper of OP-021T. The

authors wish to acknowledge the valuable technical discussions with

T. Kubota, G. Donohue, C. M. Dube, V. Panico, 1. Mantrom and 0. Hove at

Dynamics Technology. We would especially like to acknowledge the assis-

tance and cooperation of Dr. W. Madigosky of NSWC for providing much of the

materials data and instructive technical discussions.

Ackcession For_SGA&I. .' .,"TAB 0

vailabilitY Codes

'Avil end/or

Or,0

e tir

* Dynamics TechnologyDTN-8256-01

ABSTRACT

This study examines the effectiveness of elastomer coatings for specular,

acoustic backscatter reduction in low frequency, underwater applications.

Four representative elastomers were selected: Butyl B252, Neoprene W,

Polybutadiene, and Thiokol RD. Their coating reflection loss for CW and

impulse incident acoustic plane waves was examined using techniques and

computer codes developed based on a geometric acoustics approach. The per-

formance of these elastomer coatings was examined in the frequency range

from 10 Hz to 10 kHz, the pressure range 0 to 500 psig, and the temperature

range 00 to 30°C; ranges commonly encountered in oceanic applications. The

results indicate that at low frequencies (order 100 Hz), the available

elastomers, applied as homogeneous coatings up to 20 cm thick, are not suf-

ficient to obtain reflection reduction greater than 6 dB for the specified

conditions. Greater specular backscatter reduction may be achieved by

using layered, inhomogeneous coatings, but a more relevant approach for

these low frequencies may involve the examination of structural resonant

response to the incident acoustic field since the body size and acoustic

wavelength are of the same order of magnitude (Gaunard, 1977). The struc-

tural resonant mechanism of backscatter is probably dominant at low fre-

quencies.

-ii-

L EII-

Dynamics TechnologyDTN-8256-O1

TABLE OF CONTENTS

PAGE

ACKNOWLEDGEMENT5 ....................................................... i

ABSTRACT................................. .......... .......... i

TABLE OF CONTENTS ...................................................... ii

LIST OF FIGURES ................................................ iii

TABLE OF SYMBOLS .................................................... vi

1. INTRODUCTION.......-..................... o..... o............ .. I1.1 Project Objectives .........................................1.2 Background and Scope,....o..... o.....o.......... .............1.3 Conclusions ....................... o-......... .... 31.4 Report Structure...... ........... -........................ 4

2. THEORY AND IMPLEMENTATION ......................................... 2

2.1 Assumptions and Conditions ...... oo- ........ ....... 22.2 Continuous Wave (CW) Reflection Coefficient ............. ..... 72.3 Reflected Impulse Response ................................ ..2.4 Reflected Response toian Arbitrary Signal.................... 10

3. VISCOELASTIC PROPERTIES... .................................... 113.1 Background and Assumptions ................................. 113.2 Definitions and Relations ... .................... 5......3.3 Frequency Dependenc.......o .................. o.. .... 123.4 Temperature and Pressure Dependence .................. .... ... 143.5 Classification of Elastomers ..... ................. o......... 15

4. STUDY OF FOUR REPRESENTATIVE ELASTOMERS ................. ....... 174.1 Properties and Selection ................................... 174.2 Parameters and Conditions..................................... 244.3 Reflection Loss Results.. .... . .............. 264.4 Impulse Reflection Results ............................... 324.5 Limitations of the Study .................. 35

5. DISCUSSION AND RECOMMENDATIONS ................................. .375.1 Alternatives and Options................................. 375.2 Constraints for Underwater Applications...................... 395.3 Summary and Recommendations....... ...................... 40

REFERENCES .......................... ... . ...... ......... 41

APPENDIX A: FORMULATION OF THE ACOUSTIC REFLECTION COEFFICIENTAND IMPULSE RESPONSE...... ...... .......... . o Al

-iii-

4

Dynamics TechnologyDTN-8256-n1

LIST OF FIGURES

PAGE

Figure 1-1. Calculated reflection reduction for Thiokol RD withv = 0.40 and 0.44 (from Gran, 1982) ...................... 2

Figure 2-1. Coating geometry for the study ........................... 5

Figure 2-2. Scattering from a rigid cylinder with radius r(k = acoustic wavenumber) (adapted from Skudrzyk, 1971).. 6

Figure 2-3. Water gun waveform (from Buoyoucos, 1980) ......... 8

Figure 3-1. Dynamic shear modulus data (Gr = real part, Gi =

imaginary part, 6 = Gi/Gr loss factor) forunvulcanized natural rubber at 25°C (from Davey andPayne, 1964) ............................................. 13

Figure 3-2. Pressure dependence of the sound speed (cr) forButyl B252 at three different temperatures(fra Capps, Thompson and Weber, 1981) ................... 14

Figure 3-3. Temperature and frequency dependence of the dynamicshear modulus (Gr) and loss factor (6) near the transi-tion region where Tt and w are the transitiontemperature and frequency (from Snowdon, 1968) .......... 15

Figure 4-1. Master curves of the dynamic shear modulus G for Butyl3252, Neoprene W, Polybutadiene, and Thiokol RD at T100C ................................. 19

Figure 4-2. Shear loss factor 6 for Butyl B252, Neoprene W,Polybutadiene and T$iokol RD at 10°C ..................... 20

Figure 4-3. Calculated longitudinal modulus data (at I00 C) assumingconstant, real Poisson's ratio v and 6M = 6G for thefour selected elastomers used in computing reflectionloss ..................................................... 21

Figure 4-4. Calculated longitudinal modulus data assuming6M = 2

6G G ./Mr (6M << ) for the selected elastomersNote unrealistic constant Mr curves ...................... 23

Figure 4-5. Calculated longitudinal loss factor 6M for the data inFigure 4-4 resulting in negligible sound absorption

(6M << i) ................................................ 4

-iv-

hor.

Dynamics TechnologyDTN-8256-01

Figure 4-6. Calculated CW reflection loss for the selected elasto-iners at 100C ......................................... 7

Figure 4-7. Calculated CW reflection loss for the selected elasto-iners at 200C..............,.............................8

Figure 4-8. Calculated CW reflection loss for the selected elasto-nesat °C30,hers at .. ........... ...... ...................... .... 3

Figure 4-9. Sensitivity of calculated reflection loss to Poisson's

ratio at 100C and 200C for Thiokol RD.................... 31

Figure 4-10. Incident unit impulse................................ 32

Figure 4-11. Calculated impulse reflection from a 10 cm layer of theselected elastomers at 100C. The peak for Thiokol RDis wide due to FFT resolution (only components up toI kHz are included) ................................... 33i

Figure 4-12. Calculated impulse reflection from a 10 cm layer of theselected elastoiners at 200C 34

-V-


TABLE OF SYMBOLS

aT WLF frequency shift coefficient

Ca, Cb WLF empirical shift constants

c complex dilatational wave speed or sound speed (c = cr + i ci)

cG shear wave speed (complex)

G complex shear modulus (G = Gr + i Gi)

H layer thickness

I reflected impulse response

i s reflected response to an arbitrary signal

K complex bulk modulus

M complex longitudinal modulus (M = Mr + i Mi)

Pinc incident pressure amplitude

Prefl reflected pressure amplitude

R plane wave, pressure amplitude reflection coefficient

R12 boundary reflection coefficient (between ,nedium I and 2)

S(W) spectral decomposition of incident signal

T temperature

To reference temperature

t time variable

x,z position variables

6G loss factor or loss tangent for shear (6G = Gi/Gr)

5M longitudinal loss factor (6M = Mi/Mr)e incidence angle

Lame constant

V Poisson's ratio (ratio between lateral contraction and

longitudinal extension)

p density

P1 9 cl density and sound speed in nedium I (fluid)

P2' c2 density and sound speed in medium 2 (layer)

tcharacteristic time variablephase term

W acoustic frequency

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Dynamics TechnologyDTN-8256- 1

1. INTRODUCTION

1.1 Project Objectives

There is currently some interest and concern in the U.S. Navy regarding

low-frequency, active, acoustic ASW systems. If low frequency (- 100 Hz)

acoustic pulses were to be ujtilized, such systems night allow long-range

detection (because of negligible sea-water absorption) and they might be

difficult to counter with an active system onboard the target. The poten-

tial for passive counter-neasures, such as anechoic coatings, has not been

completely ruled out however. In particular for anechoic coatings, several

recent preliminary calculations (see below) have indicated a surprising

capability and it was the purpose of this investigation to refine these

calculations and extenA then to other possible coating materials.

The technical objective of thi5 study is to assess the effectiveness of low

frequency anechoic coatings on target strength reduction and make recommen-

dations concerning their development and utility. In particular, acoustic

reflection characteristics of a homogeneous viscoelastic layer (an elasto-

ner coating) at low frequencies (on the order of 10 Hz) in water are exam-

ined. The effects of viscoelastic miaterial properties and coating thick-

ness on the reflection response are analyzed. Selected elastomers are

examined for their effectiveness in this application over the range of

environmental conditions to be encountered using computer codes developed

to calculate the continuous, plane-4ave, acoustic reflection coefficient

and the impulse reflection response of a homogeneous, plane coating over-

lying a rigid, perfect reflecting structure.

1.2 Background and Scope

1.2.1 Background

Interest in low frequency, underwater acoustic absorbers was sparked by

results of a study by G. V. Borgiotti (1981) which indicated that at

S100 Hz reflection reduction on the order of 10 dB was possible with coating

-l -


thicknesses on the order of 30 cm for the elasto:ner Thiokol RD.* R. L.

Gran (1982) corrected Borgiotti's calculations and found that reflection

reduction of this level could be achieved with coating thicknesses on the

order of 5 cm (Figure 1-1). After more detailed study of the typical pro-

perties of viscoelastic materials, it has been found that the encouraging

conclusions of these two previous studies were the result of an underesti-

mate for the Poisson ratio of Thiokol RD which is about 0.495 rather than

0.44 taken by the two studies. Unfortunately, the more realistic value of

v z 0.495 results in much poorer reflection reduction as discussed later in

this report.

THICKNESS (cm.)

0 5 10 15 20

V =0.40..-z

ILt

3:-1O T = 20 0C

Figure 1-1. Calculated reflection reduction for Thiokol RD with v 0.4Dand 0.44 (from Gran, 1982)

Nn experimental vibration damping elastomer developed in the 1940's and

50's which is no longer available.

-2-

D)ynamics TechnologyDTN-8256-01

1.2.2 Scope

This study effort consisted of four basic steps. The first step was the

development of the theoretical background and basic algorithms to solve the

problem of plane wave reflection reduction from a plane layer overlying a

rigid perfect reflector. The second step involved obtaining material pro-

perty data for available elastomers, running the algorithms with the data,

and developing the final presentation format for the output data results.

The third step was to analyze these computed results and parameter varia-

tions for the selected coating materials. The fourth and final step was

the examination of application and analysis alternatives for underwater,

low frequency target strength reduction.

The task of obtaining the "complete" low frequency, dynamic viscoelastic

properties of available elastomers for the code calculations proved to be

most difficult and time consuming. Although the dynamic properties of a

wide variety of elastomers were availahle, the information for each indivi-

dual elastomer was often incomplete. As a result, certain properties had

to be estimiated based on "typical" characteristics and values for elasto-

liers. This required a more detailed study of viscoelasticity and an exami-

nation of the sensitivity of reflection reduction to these estimates by

variation of these paramneters.

1.3 Conclusions

After computing the acoustic reflection reduction capabilities of Thiokol

RD (with reasonable estimates of its material properties) and three other

representative elastomers, our conclusion is that for typical oceanic con-

ditions (00-300 C) and reasonable coating thicknesses (1-20 cm), the elas-

tome.-s considered do not provide sufficient reflection reduction in the

single homogeneous layer configuration for low frequency (order 100 Hz)

acoustics. The reflection loss was, in all cases, no more than 6 dB for

coatinq thicknesses less than 20 cm. The acoustic wavelength at 100 Hz in

-3-


the elastomer layer is about two orders of magnitude larger than a reason-

able coating thickness. Therefore, unless the acoustic wavelength in the

layer can be significantly reduced by reducing the sound speed in the

layer, the effect of viscoelastic coatings having reasonable thicknesses on

specular acoustic reflection should be negligible at low frequencies.

These conclusions do suggest that for effective low frequency, underwater

anechoic coatings, the available elastomers might be riodified to provide a

lower coating sound speed. One technique for accomplishing this is by

introducing inhomogeneities such as air voids, qhich convert energy from

dilatational modes into shear modes for which the wave speed is much

slower. Also, using such materials in coatings with a more complex geo-

netry (layering and/or selective distribution about a body), significant

target strength reduction may be achieved. Such an approach should include

modal analysis which encompasses the total structure/coating system rather

than just a simple geometric acoustic analysis since resonant interaction

of the structure with the acoustic field may be just as dominant a mechan-

is:n at these low frequencies where the acoustic wavelength is on the order

of the structure size.

1.4 Report Structure

The theory and analysis used to develop the algorithms for calculating the

continuous wave reflection coefficient, the reflected impulse, and the

reflection response to an arbitrary signal are discussed in Section 2. An

examination of the relevant viscoelastic properties with respect to their

frequency, temperature, and pressure dependence and their effect on acous-

tic absorption follows in Section 3. A parametric study of four represen-

tative elastomers is then presented in Section 4 in which the effects of

coating thickness, temperature, density, and dynamic moduli are discussed.

Lastly, observations, alternatives, application constraints, and a summary

with recommendations for further analysis are given in Section 5.


2. THEORY AND IMPLEMENTATION

2.1 Assumptions and Conditions

The acoustic reflection algorithmns were developed using the theory of geo-

metric acoustics applied to plane acoustic waves incident on a plane, homo-

geneous layer overlying a rigid, perfect reflecting foundation (Figure

2-1).

INCIDENT PLANE WAVE FIELD

Uz

, I WATER

COATING H//// / 7 '7/

RIGID FOUNDATION

Figure 2-1. Coating geometry for the study

-5-

* Dynamics Technology iDTN-8256-01

The assumption of an infinite plane layer neglects diffraction effects

around a finite body, but since the acoustic wavelength and body size are

within the geometrical scattering region, (kr > 2) (Figure 2-?), and a

coating has negligible effects on diffraction, the assumption is quite

valid for this study of anechoic coatings.

.8

.6 OM CA

IRI .4

.2 RAYLEIGH

0 I .

0 1 2 3 4 5 6 7 8 9 10

kr

Figure 2-2. Scattering from a rigid cylinder with radius r (k = acousticwavenumber) (adapted from Skudrzyk, 1971)

The plane layer represents an elastomer coating and the geometry results in

the naximum specular reflection possible since the structure is approxima-

ted by a perfect reflector. Since only specular, nonostatic backscatter is

considered, only norinally incident plane acoustic waves are of importance.

As a result, only dilatational modes of wave propagation within the homo-

geneous plane layer will be considered since conversion to shear modes

should be negligible at normal incidence.

-6-


2.2 Continuous Wave (CW1) Reflection Coefficient

The plane wave (pressure amplitude) reflection coefficient for a plane

viscoelastic layer overlying a perfect reflecting foundation is given by

the equation

R - e= 12

1 + R 12 e - 1 2

where

S H- D2 phase term

R -7 boundary reflection coefficient12 0 2

D Cos 9

2 = r) - sin 2 0

e acoustic frequency, incidence angle

PI, C fluid density and sound speed

H, P2 % c2 layer thickness, density, and sound speed

A viscoelastic absorbing layer's sound speed (dilatational wave speed in

this case) c2 is complex, resulting in a complex reflection coefficient R,which accounts for absorption. A detailed formulation of the expression

for R as a function of frequency, incidence angle, layer thickness, and

material properties is given in Appendix A.

-7-

Dynamics Technology 1

DTN-8256-O1

2.3 Reflected Impulse Response

The reflected impulse response is essentially the time series representa-

tion of the broadband reflection response of the coating. It is a compact

representation summarizing the coating response over a large range of fre-

quencies. Initially, the technique was considered to calculate the coating

response to a very short (msec) duration pulse like that produced by a

water gun which does not produce a CW signal (Figure 2-3). For long range

propagation in which high frequencies are absorbed and deeper sources are

utilized, the water gun (a cavitation device) cannot be used and signal

pulses are of much longer duration (order tens of msec). In these long

range applications, the CW (frequency) representation of the coating

response is more relevant than the impulse (time) representation. The

technique developed to obtain the impulse response from the CW results does

provide a method of calculating the coating time response to an arbitrary

pulse or signal whose transmitted spectrum is known.

WATER GUN PRESSURE WAVEFORMI I

6.0- CAVITY CAVITYGROWTH COLLAPSE

4.0-E

-2.0VALVE OPENS

VALVE CLOSESC)-2.0WGUN DEPTH: 20 ft.

HYDROPHONE DEPTH: 250 ft.. -4.0 FILTER BAND: 0- 5 kHz

SURFACE REFLECTION

5 I I I I

0 20 40 60 80

TIME (m sec)Figure 2-3. Water gun waveform (from Buoyoucos, .t z7., 1980)


The plane layer reflected response as the ratio of the reflected pressure

amplitude Prefl to the incident amplitude Pinc for an impulse (sudden on-

off pulse of unit amplitude) is given by

prefl 1 +f R( f e 'Iwi7-n c 2 o W

where 0 frequency limit of R(w) data

I fx sine + z coso - c t)c I C-- I

R() CW reflection coefficient as function of w

iR(-w) =R (w) analytic continuation for negative frequencies

x,z distance along and distancefrom layer-water boundary

tt ime

Note that the finite frequency limit wo of the integral is an approximation

of the exact impulse response (when wo = -) since information on R(w) at

frequencies above wo is not included. The frequencies above wo are essen-

tially "filtered" out of the incident and reflected impulse. In practice!,

the integral is evaluated by use of a discrete Fourier Transform (i.e., FFT

algorithm) which represents a further approximation by replacing the inte-

gration with a discrete summation. A detailed formulation of the reflected

impulse response expression is provided in Appendix A with a comparison of

computation results with an exact solution showing good agreement.

I


2.4 Reflected Response to an Arbitrary Signal

The plane layer reflected response to an arbitrary waveform or a pulse-

shaped acoustic signal can be computed by

- Wo

where R(w) is the complex CW reflection coefficient and S(w) is the complex

spectral decomposition (or Fourier Transform) of the incident signal. The

spectral decomposition of an arbitrary transmitted signal can be obtainedby various signal processing techniques (i.e., FFT) so that the reflected

response of 3 plane layer to such an acoustic signal can be predicted with

this technique. Essentially, the incident signal S(w) is "modulated" by

the plane layer response R(w) resulting in the reflected signal response of

the coating to an arbitrary incident signal. The inverse problem is also

of interest in which a known transmitted incident signal S(,) and reflected

response Is(t) are measured to find the coating CW reflection response

R

-M(-


3. VISCOELASTIC PROPERTIES

3.1 Background and Assumptions

Viscoelasticity represents a class of material behavior between that )f a

viscous liquid and an elastic solid. The assumption of linear viscoelas-

ticity is a good approximation of the behavior of most elastoners in typi-

cal stress-strain conditions. Linear viscoelasticity allows the modeling

of stress-strain behavior by systems of linear viscous elements (dashpots)

and linear elastic elements (springs) in series and parallel. For our

application, the assumption of linear viscoelasticity applies, and the fol-

lowing discussion is based on such a concept.

3.2 fOefinitions and Relitions

The single, most inportant -naterial property of a viscoelastic layer in

determining its effect on the reflection coefficient is the complex dilata-

tional wave speed c of the elastomer :naterial making up the coating layer,

assuming negligible conversion into shear wave modes near normal incidence.

The complex sound speed is dependent on the density and complex moduli of

the material. This complex sound speed can be calculated from the other

material properties by the standard relations

c2 = M. + 2 G K + G 2(1-v)G

where

p is the density

II is the complex longitudinal modulus

% is the Lame constant

G is the complex shear nodulus

K is the complex bulk modulus

v is Poisson's ratio-SI


The complex noduli quantify the relationships for the magnitude and phase

delay between stress and strain and, therefore, account for the speed and

attenutation of sound in the material. Often, the term loss factor or loss

tangent is introduced to describe the relation between the real and imagin-

ary parts of a complex modulus. For example, the loss factor for the shear

modulus is

GiS -G so that G = Gr (I + i6G)

r

where Gr = Re{G} and Gi = Im{G}. Unless the complex longitudinal modulus Mi

is known, at least two other dynamic properties (i.e., v and G, or K and r,

etc.) must be known in order to calculate the complex sound speed c. The

complex sound speed and attenuation are functions of frequency since the

complex dynamic mnoduli of elasto-ners are functions of the frequency of

stress loading.

3.3 Frequency Dependence

Usually, the available information on frequency dependent complex moduli

for elastomners is in the form of The real part and the loss factor for the

complex shear nodulus G. For this reason, the frequency dependence of the

dynamic shear modulus and its effect on sound absorption at different fre-

quencies will be discussed. The shape of the complex dynamic shear modulus

curve of viscoelastic materials as a function of frequency is quite general

and can be represented by data for unvulcanized natural rubber (Figure

3-1).

The dynamic behavior of the elastomer can be separated into four different

categories corresponding to the different frequency regions shown in Figure

3-i. At very low frequencies, viscoelastic materials behave more like vis-

cous liquids in which deformation can continue at a fixed level of stress

(i.e., creep), and viscous dissipation is the chief form of energy absorp-

tion. This type of behavior is characteristic of the "flow region".

-S?


FLOW- -RUSBERY ELASTIC I-TRANSITION - -GLASSY-1110 REGION I PLATEAU -' REGION REGION 2"S

II ,*' ', I,

E-,°, I ..*' ,

6 LS 1 1 1

-I /,, ' ' 7

Fiur 3-1. Dyn mi sha modulu dat = re lp r ,. ia in r

J . 1 ,/ .

4,."//\

part, 5 = Gi/G r loss factor) for unvulcanized natural rubberat 25°C (froin Bavey and Payne, 1964)

in the "rubbery elastic region" (at n ediumn frequencies), elastomers behave

in the rubber-like mnanner that we associate with these materials. In both

the flow and rubbery elastic regions, the dynamic modulus remains relative-

ly constant.

At higher frequencies, the dynamic behavior of elastomers passes through a

"transition region" fromn a rubber-like behavior to a glass-like be.iavior.

In this transition region, the comnplex modulus increases very rapidly with

frequency, and the loss factor reaches a maximnum. It is within this fre-

quency range where the maximum absorption for the material occurs. At even

higher frequencies above the transition region, elastomers behave in a

glassy manner mnore like an elastic solid. In this "glassy region," the

loss factor drops to very low values, and very little energy is absorbed by

the material. The real part of the shear -nodulus Gr is nearly constant and

approaches an asymptotic value at infinite frequency while the imaginarypart Gi affecting absorption decreases.

-13-

Dynamics Technology fDTN-8256-01

3.4 Temperature and Pressure Dependence

For the range of operating pressures of interest in underwater coating

applications (less than 500 psi), the sound speed of elastomers is rela-

tively insensitive to changes in pressure (Figure 3-2). By comparison, for

the range of operating temperatures 0°-30*C, the sound speed and dynamic

moduli of elastomers change considerably more. The effect of temperature

changes on the dynamic modulus of an elastomer is to shift the modulus vs.

frequency curve in frequency while preserving its shape. In fact, dynailic

modulus information can be represented by a master curve vs. reduced fre-

quency (aTw) at a reference temperature To and two empirical shift con-

stants Ca and Cb. The amount that the modulus curve is shifted in frequen-

cy (aT) to represent data at another temperature T is computed from the LF

(Williams, Landel, Ferry) equation (Ferry, 1980).

1600:-

W BUTYL B252(n

r:C

0wa-

Z 16 0 0r

0

1500aI IIII IaaIII I IIIIIII I0 2000 4000 6000 8000 10,000 PSIG

13.79 27.58 41.37 55.16 68.95 MPoHYDROSTATIC PRESSURE

S Figure 3-2. Presure dependence of the sound speed (cr) for Butyl B252 atthree different temperatures (from Capps, Thompson and Weber,1981)

-14-


Ca (T-T0 )log aT = Cb + (T-To)

where the temperatures are in units of degrees Kelvin. Normally, an

increase in temperature causes a shift of the modulus curve to higher fre-

quencies while a decrease in temperature shifts the curve towards lower

frequencies (Figure 3-3).

I" Gr

T/Tt T/

F;gure 3-3. Temperature and frequency dependence of the dynamic shearmodulus (Gr) and loss factor (6) near the transition regionwhere Tt and wt are the transition temperature and frequency(from Snowdon, 1968)

3.5 Classification of Elastomers

Elastoners can be classified as either high loss or low loss depending on

the application, operitinI temperature and frequency range. Comparing the

complex dynamiic noduljs information to classify a material as either high

loss or low loss requires comparison of both loss factor and the real part

of the dynamic nodulus within the temperature and frequency range of inter-

est. The fact that one elastomer has a higher loss factor than another is

not sufficient to classify it as 3 higher loss material. In many cases, an

elastoner with a higher loss factor than another can exhibit less damping

and energy absorption.

-15-

fynamics TechnologyDTN-1256-01

For two elastomers with equal loss factors at a temperature and frequency

of interest, the one with the lower value of the real part of the dynamic

modulus will exhibit greater absorption and damping. In general, a low

value of the real part of the dynamic modulus with a high value of loss

factor results in greater damping and energy absorption (a high loss mater-

ial). The A_)nplex modulus (both real part and loss factor) of the elasto-

,ners must be compared for the specific range of operating temperatures and

frequencies since the behavior of some elastomers is extremely temperature

and frequency sensitive.

The longitudinal modulus 4 is normally one to two orders of magnitude

greater than the shear .odulus G for viscoelastic (rubber-like) materials.

This observation is exemplified by one's experience that rubber-like

materials are nuch easier to heni (shear deformation) than to stretch

(longitudinal leformation) and by the fact that shear waves exhibit much

slower propagation speeds c G =%7) than dilatational waves in visco-

elastic matrials. For the tenperatu.re and frequency ranges of interest in

this study (0 0-30'C) and order 100 Hz acoustics, the common elastomers have

values of the magnitude of the dynamic shear nodulus on the order of 107

and 190 dyn/cm- while the !naqn -ude of the dynamic longitudinal modulus is

on the order of 1F'4 to 101 J dyn/cm2 . In these operating conditions, the

density and sound speed of these elasto:ners are nearly the same as water

(p = 1.0 gm/c;nl and c = 1.5 x 1V cm/s) so that their characteristic acous-

tic impedances (pc) are well matched for application as underwater anechoic

coatings (this is not true for applications in air in which the impedance

mismatch is a major problem).

-16-


4. STUDY OF FOUR REPRESENTATIVE ELASTOMERS

4.1 Properties and Selection

Based on the high/low loss criteria discussed in the previous section and

the availability of dynamic material property data, four specific elasto-

mers were selected to study their 2ffectiveness in low-frequency, under-

water anechoic coating applications and their sensitivity to environmental

and design changes (i.e., temperature and thickness). The four materials

considered herein are Butyl 3252, Neoprene W, Polybutadiene, and Thiokol

RD. These were selected based on their low values of the real part of the

dynamic shear modulus and high values of loss factor at frequencies on the

order of 100 Hz in the temperature range 00-30°C compared to other avail-

able elastomers.

The iqaterial property data used in this study were: density (p), real part

of the dynamic shear nodulus (Gr), shear loss factor (5r), and real part of

the sound speed (Cr). In order to obtain longitudinal wave propagation

information fro'n the shear data provided (Gr, 6), it was necessary to

assume a constant, real Poisson's ratio v over the temperature and frequen-

cy range of interest. This assumption probably predicts more longitudinal

absorption than is actually realized since it results in the longitudinal

and shear loss factors being equal (6M = 5G). At the I )w frequencies of

interest here (order 100 Hz) the error introduced by th!, i sumpt.-' hould

not affect our conclusions appreciably. Poisson's ratios for the elasto-

,hers ,ere calculated from Cr, Gr, and p data using the relation

2(l-v)G

r -(1-2v)p

assuming that c2 >> c? (which is reasonable at these frequencies). Ther Iresults of these calculations are shown ii Table 4-1. For elastoners,

Poisson's ratio is typically in the range from 0.490 to 0.499. A reason-

able estinate for Thiokol RD is then v = 0.495.

-17-


Table 4-1. Density (p), sound speed (Cr), and Poisson's ratio (v)at T 10°C, f 102 Hz for the four elastomers examined

p(gm/cm3) Cr(X 10 5 cm/s)

Butyl B252 1.17 1.58 0.497

Neoprene W 1.44 1.60 0.499

Polybutadiene 1.13 1.40 0.498

Thiokol RD 1.25 1.13 * 0.495 *

• unknown, reasonable estimate

The !waster cjrves and WLF shift constants (C and Cb) for the dynamic shear

modulus were avail3ble for Butyl 9252, Neoprene W, and Polybutadiene

(Roberts and Madigosky, 1980; and Capps, Weber and Thompson, 1981), hut not

for Thiokol RD. fata for Thiokol RD were available at three different tem-

peratures (Snowdon, 1968) and were interpolated for 10C. The different

tenperiture curves then allowed calculation of the IJLF constants for the

master curve of Thiokol RD at 100C. The dynamic shear modulus data for all

four materials are shown in Figure 4-1 followed by their shear loss factors

in Figure 4-2.

The dynamic longitudinal modulus data calculated from the results in Table

4-1 and Figure 4-1 ising the relation

M = 1-vki~-2v

are presented in Figure 4-3. The longitudinal wave speed used in the

reflection algorithns can then be found from the relation

C -1-

wo In

If 0

co o -

C3 C3

01 3 ao

(11 -l e:3J 4- 7%0 IL

0- -- -

i l I, I i l

Sol a' t) I at at at

C1NW/NC 9 r a' -IO)C~j -OL.00

C .4 of

ItI-:, ~ .0 '

CL (OL -,(.

-' I.- (.-7

am/N~ci -J C3m3/).C L ;M

1:aC - cc

at. asat a tSD a

a &S 0

II NW1NO 0

03 c

0 0

a3 -

.4= C3C

LU --

SSQJ UdH W-'tU SQ d9SL

110

- CD

~1

aA C-.40 .

010

LW I UU.J UW LJU W Jn

m IU

a U-U

LUUL

o a

lo act 0

-20

0~00

CL

c r0 0

m 0 U 0LI

00 104 )

at at t at at at4~ w

U T 1 ?t~UU~/N)O) Wt~au~/N~G)

"3 ff.

r4 .4 4

IIJ L4 ) Ln 4..

-L z C.-

- - L

mw L

00oLit I I I(.LLL I

at ~ ~ ~ OZa taat TO LU t

(ZONW/Nlo W (ZnW3/IC.4

I.A

Z Cj3 C3 Z

0 U0

- C

* C.,

Lim Lim Lit

(-3 LJ ~ -00 4-l11 ... at ata t t a a p

Itl 1 9 4T t I 1 1

(ZwG3/NOJ (ZEWO/NO)

I )->LUI ~ U

illz 1 ril il il 1 r l ti il17

C3 .4

CN LL1 11 L 1JJ

(~UW~3N)O W uEJNJO N0C3 LA- M

COLL

m 0

Slt a t a a t a t a a

- U-

-22-j

- LA-

- .4

LLL

-4-

-13 0LL. a

I--M111 I t11 i hIjI

I- 0

Ln ti aJ La. i -

uj~ -

CC UUIC3LL 0 L

-L

0 AIa 111

a- CW9'0U SS9'J *U~nI)Q mou OWiitinn

3-.


where both c and M are complex functions of frequency and temperature.

Another expression relating shear properties to the longitudinal properties

is given by

5M = 2 5 Gr

(Madigosky and Fiorito, 1q82) and results in substantially different values

for the longitudinal moduli than the ones calculated by assuming a con-

stant, real Poisson's ratio. This expression results from ultrasonic data

on liquids and polymers and may not apply at the low frequencies in our

case. Essentially this high-frequency expression results in negligible

longitudinal ahsorption (reflection loss less than 1 dB) since Mr is about

two orders of magnitude larger than Gr for elastomers. The longitudinal

moduli were calculated using this ultrasonic-extrapolated expression and

the results are displayed in Figure 4-4 followed by the calculated 5M in

Figure 4-5. The nearly constant value of Mr over frequency (Figure 4-4)

leads us to believe that this ultrasonic extrapolation is not applicable to

the present low frequency case since Mr should increase with frequency in

this region. Therefore, the longitudinal data calculated using the con-

stant, real Poisson's ratio assumptions (Figure 4-3) is used to compute

reflection loss in this study and should he valid in the frequency range of

interest.

4.2 Parameters and Conditions

For low frequency, underwater, anechoic coating applications the environ-

mental and design parameters of interest are:

- acoustic frequency

- temperature

- pressure

- coating thickness.

-24-

fDynamics TechnologyITN-8256-01

Typical ranges of values for these parameters in this application are given

in Table 4-2. The ambient qater density and sound speed were taken as 1.0

gm/cmi and 1500 m/s, respectively, and the ambient pressure was set at 0

psig since the elasto,ners were found to be quite insensitive to pressure in

the range of interest (Figure 3-2). The effects of temperature in the

range 00 -30°C and coating thickness in the range 1-20 cm on effective coat-

ing reflection reduction at 100 Hz were examined in this study. The dyna-

inic viscoelastic properties of the four elastomers examined at 100 Hz are

tabulated in Table 4-3.

Table a-2. Paraneter value ranges of interest for underwateranechoic coating applications

acoustic frequency order 100 Hz

tenperature 00 300C

pressure _ 500 psig

coating thickness 1 20 cm

Table 4-3. Oynamic modulus data for the four selected elastomersat 100 Hz for IO°C and 200C.

Gr (19' dyn/cm 2) Mr (I09 dyn/cm 2 ) 6 G or 6m

100C 20°C 10°C 200C __0C 200C

Rjtyl 1252 5.7 2.9 9.5 4.9 0.96 0.88

Neoprene W 3.1 2.4 16.0 12.0 0.25 0.15

Polyhutadiene 2.3 0.9 5.8 2.3 0.70 0.23

Thiokol RD 12.0 2.2 12.0 2.2 1.30 1.?1

-25-

Dynamics TechnoibgyDTN-3256-O1

4.3 Reflection Loss Results

The reflection loss is defined as

RL -10 log R12 (dB)

where R is the complex CW pressure amplitude reflection coefficient dis-

cussed in Section ?.2. The lower limit of RL is 0 dR corresponding to

total reflection of incident acoustic energy. The larger RL (in dB), ,he

less acoustic energy is reflected and the greater the absorption by the

coating. It is well to reiterate that the results presented are for

specular backscatter from a plane, viscoelastic coating layer on a perfect

reflecting, rigid half-space in water.

At 100C, all four selected elistoners exhibit little reflection loss at

frequencies below I kHz (Figure 4-6). Neoprene W and Thiokol RD exhibit

the lowest calculated reflection losses at this temperature due to their

high values of Mr (in spite of the relatively high value of 6 M for Thiokol

RD; see Table 4-3). Polybutadiene exhibits the qost reflection loss in

this case because if has the lowest Mr of the selected materials at this

temnperature (Table 4-3).

At 20°C, the CW reflection loss results are quite different (Figure 4-7).

Thiokol RD now exhibits the most reflection reduction since it has the low-

est Mr and highest 6M at this temperature (Table 4-3). The results for the

other three elastomers are not significantly different from those at 1OC

except that Rutyl B252 now exhibits slightly more reflection loss than

Polybutadiene in this case. At all temperatures of interest, Neoprene W

gives the lowest reflection loss of the selected materials because it has a

significantly higher Mr and lower 6m .

-26-

GC.

a~

-2 (m cm WI u? 'U *- 4 sC i i p 4

* I I.1'

I*u'

U:: -2

C2 ow40 wm C2 - 40ob ,

goalsm wlmum(901sm I1=,

- 4-1

- ~10

- - - -!

/4 C4 g*o .

vb m r - M f

2 m~ C3LA

too) t31S IAII

Dynamics Technolo ivDTN-3256-01

Comparing the CW reflection loss results at the two temperatures (10'C 3n

20'C), it is apparent that the selected ,laterials exhibit much greater

reflection loss at high frequencies above I kHz (except for Thiokol RD at

100 C). In fact, qaximum reflection reduction for these elastoners occ.,rs

in the neighborhood of 10 kOz corresponding to the quarter-wavelengtn

thickness frequency in which the elastomer coating has a "optimum" thic<-

ness to maximize reflection loss. Iso, Thiokol RD is extremely tempera-

ture sensitive, chanjing from a low loss elastomer at 10 C to a high loss

elastomer it 20'C. The other three elastomers were relatively insensitive

to temperature. Figure A-3 Jisplays the temperature and thickness depen-

dence of coating reflection loss at 100 Hz for the four elasto:ners. it

appears that Thiokol RD has in optimum coating thickness near 13 cm at 30°C

hile , it lower temperatures, the reflection loss increases with coating

thicKness. For Poljhutaliene at 11) Hz, the opti,num temperature is 100 C

since tie reflection reduction is less it boti lower and iigher tempera-

tures !Fiqure,

Classifyinkl the selected ,lastoners according to reflection loss at 100 Hz,

Thiokol R) is a hign loss elastomer at temperatures jreater than 200 C and a

low loss elastolier for tenperatures below irC. Butyl 9252 is a medium

loss elastoier ait 2,1°C and above and a low loss elasto-ner at 100, and

below. Roth :Iolybutadiene and Neoprene W have very poor reflection reduc-

tion characteristics and can be classified as low loss elastomers. None of

the elastomners provided iore than about 6 dB of reflection reduction 'or

coating thicknesses less than 20 cm (Figure 4-8).

The sensitivity of the calculated reflection loss to errors in the estina-

ted Poisson's ratio v 4s examined in Figure 4-9. Re,,ember that Poisson's

ratio for elasto,ners in tnese conditions is within the range from 0.490 to

1.499. As shown, reflection reduction is quite sensitive to Poisson s

ratio. The sensitivity of reflection reduction to density was found to e

negligible over the range from I Im/c:T3 to 2 gm/cm3 .

Im am

II

17 1 4

LL.

IMP -P In w - f C oC mc

THIL RD T=16 C FmI0 HZ.

2

-3

I.

a

1 2 1 6 8 10 12 "i 16 1 20ThMCMQESS (C)

"-.-

Z a 6 8 10 12 Ii 16 18 20

Fire 4-9. Sensitivity of calculated reflection loss to Poisson's ratiot I0'C and 20' C (---- v = 0.499, - . - v = 0.495,

v = 0.490) for Thiokol RD

NISIL O C-=I m

.= . ... , . .. . .. , - II , , , .. . I

IDynanics Technology

O TN-83256-01

4.4 Impulse Reflection Results

The reflection of an itnulbse (unit on-off pulse) from plane layers of the

four selected elastoners at 100 C and 200 C was calculated using the complex

pressure reflection coefficient vs. frequency results and the technique

discussed in Section ?.3. The CW reflection coefficient (R) data covered

frequencies tip to in kHz, so for our calculations, the incident impulse

(Figure 1-10) does not have energy at frequencies above 10 kHz. The

impulse reflection resujlts are then expressed as a pressure ratio (the

ratio of reflected pressure to incident impulse pressure) 's. time (Figures

4-11 and .1-12) or time series of the reflected pulse.

1.0

.4

I ::-.2

-.2

.004 -. 002 0 . .004 .00 ,008 .010TUE (SEC)

Figure 4-10. Incident unit impulse

-3?-

ca to c1)o40

O-'U 3WMS .. 0 1 5W3WSM

c3u -

L3-c

U-.-

14v:

t.a.C3 C3 m

coL

Ir w co C 0:r C to o C4UU 34SSS Olb aIS

.. . .. .* .... . . . . . . L

=C2 , cm tA-

S

I II

4.

C2)

C! 9-~ 0

au O

C2)

. _ _ ._ _ .. .. .. . a

- 4-I I I I.

C I.LUI GSS5 "- WII=C WMSa49U4-


Since the elastoners exhibit larger reflection reduction at frequencies

above I kHz, the impulse reflection results are much better than for 100 Hz

CW. The great difference between the results at J1OC and 20'C for Thiokol

RD clearly denonstrates the large temperature sensitivity of its reflection

response. The other three elastomers do not exhibit nearly as much temper-

ature dependence in the impulse reflection results. Note that these

results are for an ideal incident impulse (with frequency components above

10 kHz filtered out) rather than a realistic impulse which has some charac-

teristic frequency and time width. The reflection of a realistic impulse

or signal of arbitrary shape can be calculated using this technique (dis-

cussed in Section ?.4). These impulse reflection results provide a :neasure

of the total broadband reflection response of a coating, and they exemplify

the capaoility to calculate the coating tine response to an arbitrary

acoustic signal *Jsinqg this technique.

4.5 Limitations of the Study

The major limitation on the present study was the availability of elastoner

dynamic properties. This limitation was overcone by combininq available

data to ohtain reasonable estimates for the unknown naterial properties

(i.e., Poisson's r3tio) at the temperatures and frequencies of interest.

Four elastoners were chosen to provide a cross-section of commonly avail-

able materials that might be used as anechoic coatings. Both Neoprene W

and olybutadiene represent low loss elastomers in our conditions. At tem-

peratures above 20'C, Butyl B252 represents a mediun loss elastomer, and

Thiokol RD represents a high loss -lastomer. At temperatures below 100 C

all four elastomers can be considered low loss.

The dynamic naterial properties available were limited to frequencies up to

10 kHz (for the temperature range of interest) so the effects of absorption

at higher frequencies are not considered. This is a good apnroximation for

long rang? propagation in the ocean where high frequency acoustic wave com-

ponents are attenuated significantly. Also, in oceanic applications at low

-35-


frequencies on the order of 100 Hz, the complete backscatter response of a

coating on a structure whose size is on the order of an acoustical wave-

length nay not be accurately modeled by the response of an infinite plane

layer because other backscatter mechanisms iay be important. Instead, this

study examines the reflection reduction effectiveness of various types of

elastomers in the specular reflection backscatter regime. The plane layer

reflection is a good :neasure of the specular reflection reduction of these

elastoners for application in anechoic coatings regardless of struct,re

size or shape. The study, therefore, is most useful for applications such

as material selection where specular reflection reduction by a honoqeneojs

coatinj is of primary concern.

-36-

Dynamics Technology

DTN-3256-01

5. OISCUSSION AND RECOMMENfATIONS

5.1 Alternatives and Options

From the results of this study, we find that ,lastomer coatings used in the

simple homogeneous, single layer configuration do not provide significant

low frequency acoustic, specular backscatter reduction for coating thick-

nesses of 20 cm or less in the ocean. At low frequencies (on the order of

100 Hz) in the ocean, the acoustic wavelength is two orders of magnitude

larger than the typical coating thickness. Since the longitudinal wave

speeds in the elastoners are almost the sane as the sound speed in the

water', the elastoiaer coatings are incapaDolV of pr'viding significant

absorption at these qavelengths. In order to increase the absorption of

incident acoustic energy, the acoustic wavelength within the coating can be

reduced by node conversion of longitudinal wave energy into shear wave

energy For which the propagation speed is :nuch slower. This effectively

reduces the coating sound speed so the acoustic energy effectively "sees"

nore coating and absorption as it propagates at the slower speed.

One way to achieve a lower sound speed in the elastomer coating is to

introduce inhomogeneities such as air voids which convert acoustic energy

to shear nodes of propagation. There is a trade-off involved in this

approach. As the effective sound speed in the coating is reduced, the

coating absorption capability is increased, hut the impedance (pc) rismatch

between the water and coating is increased. This impedance mismatch causes

a portion of the acoustic energy to be reflected directly from the water-

coating interface without propagating rand being absorbed) in the coating.

Further, such coating designs may be iore sensitive to pressure changes.

Clearly, there is sole optinun coating density and sound speed that mini-

nizes the total acoustic energy reflected from both the water-coating

boundary and the propagation through the coating and reflection from the

structure (Scharnhorst, 1979).

-37-


Multi-layer coatings may also help to reduce the impedance mismatch problem

of introducing voids by matching the pc impedance at the water-coating

boundary and allowing a transition to lower sound speed and greater absorp-

tion. Such an approach has been examined at high frequencies (greater than

I kHz) and found to be quite effective (Madigosky, 1981), but its effec-

tiveness at low frequencies (below I kHz) is still in question. The high

frequency, nulti-layered, inhomogeneous elastomer coating approach relies

chiefly on quarter wavelength attenuation within the layers to maximizereflection reduction. Comparable levels of anechoic effectiveness should

not he expected at low frequencies since the layer sound speed would have

to be reduiced to about 100 m/sec or less for a 20 cm thick layer in order

to take advantage of the quarter wavelength effect at 100 Hz.

Instead, at low frequencies, an analysis of the structure-coating system

interaction with the acoustic field in the water may be more appropriate

since the acoustic wavelength in water is on the order of the total struc-

ture size and specular reflection might not be the primary backscattering

!nechanism. In fact, resonant interaction of the coating-structure and the

acoustic field may cause backscatter greater than that predicted by specu-

lar reflection alone (Gaunard, 1977). There are indications that at these

acoustic wavelengths, the dominant iechanism for backscatter is not specu-

lar reflection but resonant structural vibration and reradiation by the

structure (Gaunard and Ka.nir s, q82). If this is the case, a modal analy-

sis approach to examining the effects of low frequency coatings is moreappropriate than the geonetric acoustics approach of this study. The coat-

ing is then no longer an "anechoic" coating in the sense of reducing

reflection, hut serves more to modify the modal response of the structural

vibration and reradiation.


5.2 Constraints for Underwater Applications

In the pressure range for underwater anechoic coating applications (0-500

psig), the common homogeneous elastomers are essentially insensitive to

pressure changes. Instead, the primary sensitivity to depth changes is due

to changes in seawater temperature (within the range 00-300C). The elasto-

ners with broad transition regions and broad loss factor vs. frequency

peaks tend to be less temperature sensitive than those with sharper loss

factor vs. frequency peaks (i.e., Thiokol RD). This means that the elasto-

;ners which tend to be less temperature sensitive also tend to be less fre-

quency sensitive and would be advantageous for undersea applications if

they can provide significant reflection reduction. Unfortunately, the

elastomers e-anined do not provide significant reflection loss at frequen-

cies below 1 kHz throughout the range of application conditions.

If the coating thickness were not limited, sufficient anechoic response

could he accomplished but only at much greater thicknesses than the range

examined (1-20 cm). The permissible coating thickness is limited mainly by

the coating density (buoyancy considerations) and hydrodynamic considera-

tions. Most common elastomers have densities slightly greater than water,

and if voids were introduced, their densities would decrease. If buoyancy

was the only factor liniting coating thickness, very thick inhomogeneous

(void) coatings would be permissible. The effects of the added bulk, mass,

and compliance on hydrodynamic performance would have to be examined for

such thick coatings. It appears doubtful that any available elastomer tused

as i homogeneous coating of the thickness considered would provide suffi-

cient specular reflection reduction at low frequencies over the temperature

range of interest. Thiokol RD does provide adequate reflection loss at

20'C and above, bjt it is extrenely temperature sensitive and, therefore,

not suitable for these applications unless the coating te,nperature can be

maintained above 200C (by utilizing waste heat from the vehicle's power

plant, for example). If maintaining the coating temperature is considered,

availability of sufficient thermal flux would have to be examined.

-Iq

9ynamics TechnologyITN -256-)i

5.3 Summary and Recommendations

In summary, we have found that the commonly available elastomers are quite

ineffective in reducing specular reflection at low frequencies (order 100

Hz) f)r the tenperature range of interest (0°-30'C). Thiokol RD does pro-

vide adequate reflection loss if the coating temperature can be maintained

above 20°C, perhaps by utilizing waste heat (from exhausted power plant

cooling water). Introduction of more complex coating geometries, such as

inhomogeneities and layering, may improve coating effectiveness in specular

reflection reduction, but if the acoustic wavelength is on the order of the

body ;ize, resonant response of the whole structure systen may be the domi-

nant backscatter mechanism.

The geoletric acoustics analysis usel in this study for specular reflection

reduction is not relevant to the case where structure vibrational response

is the dominant hackscattering mechanisn. Instead, a modal analysis

approach to the total structure vibrational response with consideration of

coating, structure, and internal fluid properties, geometries, and coupling

would be necessary. The iajor mechanism in reducing backscatter in this

case would be vibration damping rather than coating absorption of incident

acoustic energy as in the case of specular reflection reduction examined by

this study.

.Ir


REFERENCES

Borgiotti , G.V. (1931) "5-'fectiZeness of Acoustic 4bsorbers at Low AcousticFrequencies," Inter-office Memo to J. C. Nolan, IDA.

Buoyoucos, J.V., McLaughlin, J.K., Jr. and Selsam, R.L. (1980), "The HYDRO-STHO K Water -un," Paper at Soc. of Exp1. Geophysicists, Tulsa, Oklahoma.

Capps, R.M., Weber, F.J. and Thompson, C.M. (1931) "Handbook of Sonar Tran-,-ducp' Paas-i'e 'aterials," NRL Memorandum Report 4311.

Davey, A.B. and Payne, A.R. (1964) Rubber in Engineering Dractice, PalmertonPubl. Co., N.Y., p. 36.

Ferry, j.0). (1q08) Viscoelastic Properties of Dolyiers, 3rd ed., John Wiley &Sons, N.Y., pp. 264-290.

Gaun,3rl, G... (1977) "Sorir ?rO.S3 Sectio n of a :7oated loZlow CyZinde' -nWzter," Jour. Acoust. Soc. Am. 61(2) :360-368.

GaunarJ, G.D. and Kalnins (1982) " ei3oni-es itn tke Sonar ?rose Sections,ei ,oZeiIZ -)'1- LIeZ, " Iqt. Jour. Sol ids Structures 13(12):1083-1102.

Gran, R.L. (1932) "Zo?,-Fre7 wn'f 4cowty A1 br '. iaZs," Internal Memoto O.R.S. Ko and R. Chapkis, Dynamics Technology, Inc.

4adigosky, W.M. (1981) "De-e!'goent )f a'odzTh i.neckoi, ,7oating far Un2er-0-t1,O '1e (U)," Proceedings of 34th Navy Syiposiun on Jnderwater Acoustics,Vol. IV (U), pp. 409-119.

Roberts, O.J. and Madigosky, W.M. (1980) "Dyn iVi coozstic Properties ofMiter-iZs for Underwoater Acoustic Appictlons, Part [Ti, " NSWC TR80-425.

Scharnhorst, K.P. (1979) "'ptimal Distribution of 7eno:t and )i Zatztion !o.11-!us ;n -nhomojen .ous Layers," Jour. Acoust. Soc. A-n. 66(5):1526-1535.

Skuirzyk, F. (1971) The Foundations of * coustics, Springer-Verlag, N.Y.,p. 448.

Snowdon, ,.C. (1968) Vibration and Shock in Pamped 'lechanical Systems, Johniley I Sons, N.Y., p. 3.

-41-

APPENDIX A.

FORMULATION OF ACOUSTIC REFLECTION COEFFICIENT AND IMPULSE RESPONSE

A.1 [ntroduction

This Appendix sunmarizes part of the analysis needed to support the COAT

project. Although the results were derived for COAT, they are quite

general and applicable to iany other problens. The general expression for

the acoustic plane wave reflection coefficient of a plane layer is derived

(using a wave number natching approach) and applied to a viscoelasti c

layer. The results of this derivation have been inplemented in) the FORTRAN

code program COAT which calculates the total reflection coefficient as

function of layer thickness, incidence angle, frequency, and ;iatarial pro-

perties (at a given tepnperitJre).

The layer (reflected) inpul se response is then developed in general form

and application to real proolems of viscoelastic layers is discussed. The

technilue has been inplenentel: in the FORTRAN program IMPULSE which uses

the reflection coefficient lata ,ieterined )y COAT to calcil ate the inpulse

response for a viscoelastic layer. The results from IMPULSE are approxina-

tions of the actual response, ani the effects of the finite FFT approxin!la-

tion used -iust )e analyzed.

The results of applying the techni ue on an l astic layer are discussed in

an exa,nPle. The COAT projrain provides the reflection coefficient data

needed as input into the IMPULSE program. The example shows excellent

agreement ,ith theoretical predictions for reflected pulse sparing and good

agreement for the reflected pul se anpl i tudes accounting for corrections

issociatel with the finite FFT technique.

,.tI

A.2 Paraiieter List

Fluid:

density Pl

sound speed cI

Viscoelastic Layer:

density P 2

sound speed c2

thlickness H

dynamic shear nodulus

Poisson's ratio v

shear danping factor

comple-x Young's molulus E

Rigid (Base) Material

density P3

sound speed C3

Acoustic Plane Wave:

wave number k=, /c

radian frequency w

angle relative to boundary e

-A2..

A.3 CW Reflection Coefficient

A general ,expression is derived for the plane wave (pressure) reflection

coefficient af a plane layer separatinj two :ther media. This qener3l

reflection coefficient is expressIi; is a finction of frequency incidence

angle 01, an] naterial properti s - ic ). This jeneral result is then

applied to the case if a plane oiscoeIastic layer on a perfectly reflectin-.

base naterial in wat.r. Thie v.iter is Jesig]nated as ymedian 1, the visco-

elastic layer as ,ielium ?, and the 1,-se iateril is ;iedium 3 (Figure A-I).

A.3.[ Derivation of the General Expression:

By eXmiflilj the reflection and refraction of the plane ,ave dt the two

boundaries (12 and 23) aetween the three iedia (Figure *\-1), the total

plane wave reflection coefficient for the layer is found to b,_

R R + \ T , -i 2 , +i2 12 23,21 12'23 21 ?3 ..

where ' hij = oundary reflection coefficient for pressare wave triveling

fron tiedian i towarls nedi an j

Tij boundary transmission coefficient for pressure wave traveling

from nediun i to :nediun j

Hk9 cos 32 represents the phase shift in the layer of thick-

ness H (where k2 cos 02 is the vertical component of wave-

nuoner in the layer).

otice that the expression for R is in the form of a geometric series where

rn (1-r) -

n=O

-A3-

so that the total reflection coefficient becolles

R R2 T2 R2 e - i 2 R R e - i 2 5

12 12 23 R= R e 1 3-21 R23 -i2n] T2 I

TR T e-iUT 1223'21R 1I2 +

2(1 - R R 23i25

?1 23

Since TI T1 1-R 2 and R2=-1,the expression is therefore

R= 2 + 23e

I + R12R23 e-

This is the general expression for the plane wave (pressure) reflection coef-

ficient of a plane layer separating two other media. R is a function of inci-

dence angle o1, frequency w, and iaterial properties (Pl,c 1 ,P9,c 2,p3,c3)

through the expressions for phase shift $ and boundary reflection coefficients

R12 and R23 given

=H LL n 2- sn2c i12 1

R ij cos - 4n? - sin 2e i

n. cos oi + 4n?. - sin 2 0.

-A4.,

where q = layer thickness

Inij = Pj/pi density ratio

nij = ci/ci index of refraction

i = 1,2

j = 2,3.

A.3.2 Application To A Viscoelastic Layer

In the case of a viscoelastic layer on a rigid base :naterial where

P2 c2/o 3 c3<<, R23+I (hard boundary with no phase inversion on perfect

reflection). For viscoelastic inaterials, the compressional wave (sound)

speed c. is a fjnction of material properties (,which are dependent on

frequency w) such that

c= (1-v) E -1/2

2 T 777+ v)(1-2v) P _?

(notice that since c? = c2(',O), the material is dispersive). Therefore, for

a viscoelastic layer separating water and a perfectly reflecting, rigid

hase material, the plane wave reflection coefficient becones

-i _R R1 + e12

1 + R12 e

where H D2 phase shift term

1 2

12 boundary reflection coefficient12 0 0 2

-A5-

D Cos '

(' v) comnpressional wave speed

E =E r (1415) complex Young's 'nodullis

Er = 2.± (1+v) real part of Young's nodulus

v = constant Doisson's ratio

' = .()dynanic shear riodulus (real)

14 loss factor

(notice that R is comnplex and accounts for absorption and attenuation due

to the viscoelastic layer).

-A6-

A.4 Impulse Response

A general expression of the impulse (reflected) response of a plane layer

for an incident plane acoustic impulse is derived using the CW reflection

coefficient of the previous section. A nethod for finding this (reflected)

response for viscoelastic layers in real conditions is then discussed.

A.4.1 General Impulse Response Integral

The incident pressure field of a harnonic ,plane wave of unit amplitude can

be written

inc ikl(xsine 1 -zcoso 1) i t

and the corresponding reflected field is

ik1fxsino I + zcose1) -i'dt~refl Re

(Figure A-2) where R is the total reflection coefficient (given in the pre-

vious section). The impulse response (general) is found by integrating the

reflected field over all frequencies so that

I +M R e ik,(xsino1 + zcosO,) -iLtd,I2x f R e

and since k, c/CI, the response integral can be expressed as an inverse

Fourier transform of the form

I() L-- ( e R()e dw

.,here R(o) = CA reflection coefficient (previous section)

T L (xsino1 + zcoseo _ c t).

-A7,,

Ft

A.4.2 Solution For A Viscoelastic Layer

To solve the response integral 1(r) for actual materi3l in real conditions,

the FFT method appears to be the most efficient since an analytical solu-

tion is not probable due to the complex functional dependence of R on W

(described in the previous section). The frequency dependence of the layer

material properties p(,o) and 6(t) are critical in determining whether or

not the integral 1(r) is integrable in its present form and what ninimui

and ,naximum frequency limits are appropriate for the FFT to obtain an ade-

quate approximation of the integral. UIsh, since the integration is taken

fromi negative to positive frequencies, and the material properties are

defined only for the positive frequencies, values of R(w) must be extrapo-

lated for negative frequencies.

In order to find the values of R(w) for negative frequencies, the observa-

tion that (in reality) the impulse response is real only (not complex) is

,ised to determine the .vn/odd characteristics of R(,). The integrand of

I(t) is a complex expression

Rei = Re {Rel :dt' + i Im {Rel '° tl

For the integral 1(t) to be real only, Tm {Rel i u T must be an odd function

(whose integral from -- to + is zero). Since Re{e1 '} is even ankl

I.{ oei '} is odd, then Qe{R} miust be an even function and Imn{R must be an

odd function. Therefore, the value of (w) for negative frequencies can be

extrapolated from the results of R(w) for positive frequencies by applying

the knowledge that the real part of R(i) is an even function and the inagi-

nary part is an odd function. This can be expressed as

Re{R(-:j)} = Re{R(,,)} even

Im{R(-, )} = -Im{R(w)} odd

or R R

-A8-

where the * superscript denotes the complex conjugate.

The minimum and maximum frequency limits for the FFT are determined by the

material properties data available. Extrapolation of the material proper-

ties data beyond the frequencies for which they are available (when greater

accuracy in the impulse calculation is needed) can be based on experimental

observations and a physical understanding of the important processes. The

effect of approximating the impulse response integral with a finite FFT

must still be determined. The correction coefficient for the reflected

response to a unit amplitude imnpulse is dependent on the frequency limnits

used in the finite FFT approximation.

-A9-

A.5 Application of Technique

The technique of calculating the reflection coefficient (fron material pro-

perties) and the reflected impulse response of a plane layer has been

applied to the case of an elastic layer for 4hich the exact theoretical

solution is tractable. In this way, the technique, discussed in the pre-

vious sections, can be conpared with the exact solution tz find the degree

to which this finite FFT technique approximates the expected reflected

response.

The programs COAT and IPULSE have been tested for a N3 cm thick elastic

layer with E = 2.83 x IrV dynes/cm2 and v = .44 for a unit i pul se at nor-

mal incidence. The density of the layer was taken to be twice that of tne

first inediun (P2/ 1 2). The results (calculated hy COAT) for the real andimaginary parts of Z (the reflection coefficient of the layer) as a func-

tion of frequency (up to 104 Hz) are plotted in Figure A-3. The reflected

response to a unit impulse (calculated hy IMPULSE) is plotted in Figure

A-4. The FFT size was 2043 (for a full frequency range of 108 Hz) with

cosine tapering of 101, on each end.

The exact theoretical prediction for this nor,,nal incidence case is given in

Figure A-5. The theoretical prediction gives a reflected pulse spacing of

about 1 msec and reflected pulse amplitudes (ratios of reflected and inci-

dent amplitude) of -0.561, 0.685, 0.334, 0.216, 0.121, 0.068, 0.038, etc.,

respectively. Comparing the expected (theoretical) result with the IMPULSE

calculation (Figure A-4), we see that the (IMPULSE) technique correctly

predicts the pulse spacing and closely approximates the amplitudes of the

odd pulses, but the even pulses (starting with the first positive puise)

show much less agreement in amplitude. Increasing the size of the FFT (the

frequency resolution of the data) did not significantly affect this discre-

pancy between odd and even pulse amplitude approximations, but increasing

the frequency range (and limit of the FFT) up to 105 Hz eliminated thisdiscrepancy at the expense of increasing the error for the odd pulses

(Figure A-6).

-A10-

%L

The results of this -xample indicate the effects of approximating the

impulse response integral with the finite FFT technique and possible

.ethods of correcting for the discrepancy (i.e., increasing the frequency

limits to reduce the ,)Jd/even pulse error). The COAT/IMPULSE technique is

shown to be a good predictor of the expected (actual) reflected impulse

response given the geomnetry and material properties of the layer jf

interest.

-All-

A11

AMPI.lTUtE PI I 3T 7 R32 3Z

(LAYER) e2

Fiure A1. SceaicoPlane layer totne a l reflectedn. er

9 ~ ~ - 12-I-N

Frequ ncy Iliz

1- I II

• r \ii\ III

Hquirek A-3 Feunydpnec ofrf ct nce ffiiet

A 3-iiiF \ i I

o . II : U ,.

: -. it-IIit

IH.1 \", I ...

/ I r

I " I\. . .. ,i"

.-cueAXFeuec eedneo relcto cofint

.i- l 3-

.5 1 " I i i | " I i I I I " I

(0.685)

(0.384) -

o [(0.216) I

0.121)I (0.068) t

II(0. 03S)

i--.z "=

- '- -ILnLn

I-L (-0.561)

-2 -1 0 1 2 3 4 5 6 7

TIME (MSEC)

*theoretically predicted reflection impulse amolitudes

are shown in parentheses.

Figure A..4. Reflected impulse response of layer calculatedusing the finite FFT technique on the reflectioncoefficient result in Figure A..3.

-A14-

,/. 1 4

o- e s Ct-y

- . v.. C..vy,. = L .Li L . Lj

- V .j - ) L j-]

II

1.0

AA

idu/ I /III / / jI7 f',; 'i'/i///iit/Ii = 1

Figure A..5. Theoretical calculations for the expectedreflected impulse response of the elastic layer

-A15-

U

rF

2 i

LzU

LU

-.4r

II

< r

TIWE (SEC)

Finure A\-6,. Calculated reflected impulse response usina a

Figure A-4,

-.A16-

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