ELSEVIER

Applied Acoustics 43 (1994) 141-148 © 1994 Elsevier Science Limited

Printed in Great Britain. All fights reserved 0003-682X/94/$7.00

Examination of Acoustic Behavior of Negative Poisson's Ratio Materials

Barba ra Howel l , Pa t P rende rgas t & Lar ry H a n s e n

Annapolis Detachment, Carderock Division, Naval Surface Warfare Center, Annapolis, Maryland 21402, USA

ABSTRA CT

Negative Poisson's ratio (NPR) foams have been predicted to have un- usual acoustic properties. To measure these, polyurethane foam was cho- sen to serve as a model system. Negative Poisson ratios were produced in open cell, reticulated polyurethane foams by heat setting the foam which had been three-dimensionally compressed 3.7-fold. Acoustic reflection measurements were made on unconverted foam, NPR uncovered foam, and on NPR foam with an unattached and attached cover. Foams tested had pore densities ranging from 25.4 to 254 pores per linear cm. NPR foams absorbed better than unconverted foams at all frequencies. Smaller pore- size NPR foams absorbed sound more efficiently at frequencies above 630 Hz than did those with larger pores, and those with covers were better sound absorbers in the frequency range 250--1000 Hz than the uncovered NPR foams. Unidirectional compression to one quarter of the original thickness reduced the Poisson ratio to zero and caused the foam to absorb nearly as well as did creation of the negative Poisson's ratio.

I N T R O D U C T I O N

The purpose of this investigation was to determine whether foams with negative Poisson's ratio (NPR) have better acoustic absorbing properties than do comparable foams which do not have negative NPRs. Polyurethane foams were used as a model system to study this effect.

Open-cell, reticulated polymer foams can be used to prepare N P R ma- terials. 1 When compressed and heated, the ribs of these foams are locked into a collapsed conformation, but when the foam is stretched, the ribs straighten, causing an increase in size perpendicular to the stretch direc-

141

142 B. Howell, P. Prendergasl, L. Hansen

tion (a negative Poisson's ratio). Foams for this investigation were three- dimensionally compressed 3.7 fold by heat setting at 127°C in two suc- cessive compression steps.

Although sound absorption in foams is usually due to viscous interac- tion between air and cell ribs, Lakes 2 has predicted that microvibration of re-entrant (NPR) foam ribs will result in very low transmissibility of acoustic waves. For this reason measurement of the acoustic absorption properties of unconverted and NPR polyurethane foams was undertaken and is described as follows.

E X P E R I M E N T A L t

Materials

Polyurethane foams used for preparation of NPR materials were reticu- lated, open cell acoustic foams obtained from Scotfoam Co., Chester, PA, USA.

Acoustic measurements were made for foams with 25 (SIF-10), 76 (SIF-30), 110 (SIF-40), 200 (SIF-80), and 250 (SIF-100) pores per linear cm. (The number of pores per linear inch is given in the foam designa- tion, e.g., SIF-30 foam has 30 pores per linear inch.) Tests were run on the unconverted material and on the material converted so as to give a negative Poisson's ratio, with and without a covering layer of polyethy- lene. Some tests were run with 100 tzm thick (10 -3 kg/m 2) polyethylene film and some with 50 /xm (0.5 x 10 3 kg/m 2) polyethylene films facing the sound source. Both surface density values are less than 0.0085 kg/m 2, the upper surface density limit given by Andersson. 3 For some tests the film was unattached, and for some it was attached by heat treatment to the foam. Comparisons were made to a 230 (SIF-90) pore per linear cm foam which had been compressed to one quarter of its original thickness (a felt).

Lower-frequency acoustic measurements were performed on cylindrical samples 10-5 cm in diameter and 3.2 cm deep. Cylindrical samples 2.9 cm in diameter by 3.2 cm thick were used for the higher-frequency set of acoustic measurements.

Light microscope photographs were taken of the unconverted foam and of the NPR foam at a magnification of 20x. The porosity of a foam

t To describe procedures adequately, it is occasionally helpful to identify commercial products and equipment. In no case does such identification imply Naval Surface Warfare Center recommendation or endorsement, nor does it imply that the item is necessarily the best available for the purpose.

Acoustic behavior of negative Poisson "s ratio materials 143

sample was estimated by weighing the foam, measuring its volume, and making use of the density of polyurethane (1.05 g/ml).

Poisson's ratios were found by placing pieces of foam approximately 2 cm × 2 cm × 8 cm on an overhead projector so than an enlarged image was formed on a screen. Strip thickness and length were measured on the screen with a meter stick before and after stretching.

Acoustic measurements

A standing wave apparatus (B&K Type 4002) was used to measure the acoustic absorption coefficient and the acoustic impedance of samples of the foam materials. 4 The required calculations are well known. 5,6'7 The established octave band or one-third octave band center frequencies are used for these measurements, to be consistent with the literature.

Absorption measurements

Measurements were made at normal incidence at various one-third oc- tave band center frequencies in the frequency range 100-6300 Hz. At each frequency, the first maximum was located and the sound level set to a known value. The first minimum was then located and the correspond- ing sound level was measured and recorded. The absorption coefficient was calculated for each data point. For baseline measurements, only the metal sample holder was in place.

Films that covered the foam in covered and attached tests were of two thicknesses.

Measurements between 100 and 1600 Hz were made using a 100-mm diameter tube, and those between 2000 and 6300 Hz with a 30-mm dia- meter tube.

RESULTS A ND DISCUSSION

Photographs of the unconverted and NPR foam, and of a comparable foam (a felt) compressed to one quarter of its original thickness, are shown in Fig. 1. Comparison of the unconverted foam (Fig. 2(a)) with the felt show that felt openings are flatter, and in general they appear to be smaller than in the unpressed foam. The NPR foam merely appears to have smaller pores than the other two, and the ribs are sometimes bent.

It should also be mentioned that when the NPR materials were stretched by more than about 10%, they began to exhibit a positive Poisson's ratio.

144 B. Howell, P. Prendergast, L. Hansen

I

(a) (b)

!

(c)

Fig. 1. Comparison of the microstructure (20-fold magnification) of (a) the unconverted 254 pores per linear cm (100 ppi) foam, (b) the negative Poisson's ratio foam, and (c) the

229 pores per linear cm (90 ppi) felt.

The porosity of polyurethane was calculated from the foam density and the density of polyurethane, which was taken to be 1-05 g/ml.

Measured values of the absorption coefficient were plotted against one- third octave frequencies to compare foams of different pore densities with and without film coverings. Plots were also made to compare NPR and unconverted foam samples. The plots are described below.

It was found that a peak appeared in all the data, including the base- line data, at 315 Hz. This peak was considered to be an artifact caused by tube resonance. Damping the tube, changing the excitation amplitude, and filtering failed to eliminate the effect. Therefore, all data for 315 Hz was replaced by the average of the value at adjacent points (250 and 400 Hz).

The first plot (Fig. 2) compares SIF-30 unconverted foam to NPR foam which is uncovered, covered with an unattached film, and with an

Acoustic behavior of negative Poisson's ratio materials 145

0.9-

0.8-

0.7-

0.6- < -1- Q. 0.5- ._1 <

0.4-

0.3-

0.2-

0.1-

Fig. 2.

A ac::a::::e0 Cov

~ :aseline 1~ 125 t£)0 2~ 250 3;5 400 500 630 800 1()00 1:~ 1 ~ ) 2 ~ 2 5 0 0 31'504(~ 5()006~ '

FREQUENCY (HZ)

Absorption coefficients (alpha) for SIF-30 polyurethane foam as a function of frequency,

1

SIF-90 Felt 0.9

Una~aehed Cov

O.8o7 A~ached C

0.6

(~1 0.5 <

0.4

o.2°3 F \ Unconve~ed

Basehne 0.1 ~

Fig. 3.

1~ 1~ 1~o ~ ~o 3;5 ~ ~o ~ ~o 1~ 1~ 1~3o ~,oo31'5o,.~oo 5~oo ~oo FREQUENCY (HZ)

Absorption coefficients (alpha) for SIF-80 polyurethane foam as in Fig. 2, with SIF-90 felt in addition.

14(~ B. th,wc/L P. Prcnde~:~ast, L. Hun.sen

<r. "1- 13.. ,_J <

o9-1 SIF-IO0 ..... ~ ..... ~ k , . . . . Z~ / " . . . ~ d h ~ - , ~ ~ : ~ > ~ . , \

084

07~

06- -

05 J

o.4 i. i

o,a-4

i 1

100 125 1 ;0 2;0

/ / / / z

j7

j ~ SIF-10

,, BASELINE

2~o 3'15 ~o 5~o 6~o 8~o 1~o ~2so' ld~ 2 ~ 2~oo 31'5o 4&o ~;~ 63®~- FREQUENCY (HZ)

Fig. 4. Absorption coefficients (alpha) for uncovered NPR foams of different pore sizes and for the SIF-90 felt. (Measurements on the 100 ppi foam were made by Noise Unlimited,

Somerville. NJ 08876.)

attached film. It can be seen that there is a definite improvement in ab- sorption in the frequency range above 200 Hz for the N P R uncovered foam compared to the unconverted. Foam with an attached cover ap- pears to work best between 200 and 1000 Hz. For this, above 1000 Hz the curve tends downwards , but has peaks at two of the higher frequen- cies.

In the second plot (Fig. 3) SIF-80 foams are compared with the base- line and with the SIF-90 felt. The results are similar to those found with SIF-30 foam in that the N P R foam shows a similar improvement in the 200 to 1600 Hz range. At frequencies below 200 Hz, all the curves con- verge and show poor absorption. At high frequencies, N P R foam with- out a cover and the felt had the best absorption.

The third plot (Fig. 4) compares foams of various pore densities which have an open surface facing the sound source. It can be seen that the ab- sorption generally increases with increasing pore density. The curve for the SIF-90 felt compares favorably with the SIF-80 N P R foam at fre- quencies below 700 Hz and exceeds it at the higher frequencies, but ab- sorption of the N P R SIF-100 foam is better at frequencies above 900 Hz than that of the SIF-90 felt. Comparable absorpt ion of the tile and the N P R foams is useful information because the one-dimensional compres-

Acoustic behavior of negative Poisson's ratio materials 147

0.9-

0.8-

0,7-

0,6 ~

< "1- 13_ o.5- - J <

0.4-

0.3-

0.2-

0.1-

SIF-1

~ ~ ' ~ S I F - 3 0 S IF -45

>e_______>e__~ H _ _ ~ ~ Baseline

FREQUENCY (HZ)

Fig. 5. Absorption coefficients (alpha) for NPR foam with unattached film coverings.

sion required for felt production allows easier production of continuous or large sheets of the material.

The fourth plot (Fig. 5) compares foams of various pore densities which have an unattached polyethylene film covering, Absorption de- creases above 400 Hz for the SIF-10 foam and above 1000 for SIF-30 foam.

CONCLUSIONS

Foams with a negative Poisson's ratio were shown to be better acoustic absorbers over the entire frequency range of 100-1600 Hz than uncon- verted materials.

At frequencies below 200 Hz, all absorption curves converged and showed poor absorption, but an unattached polyethylene covering on the foam improved absorption below 500 Hz. At frequencies above 630 Hz, uncovered NPR foams were superior and the foam with the smallest pore size showed the best absorption. Compression of the foam in only one dimension decreases the Poisson's ratio and has nearly the same influence on acoustic properties as production of a negative Poisson's ratio foam.

Acoustic absorptions found for the different materials investigated furnish guidelines for selecting materials to provide absorption in a particular frequency range.

148 B. Howell. P. Prendergast. L. Hansen

ACKNOWLEDGEMENTS

Research support from the following sponsors is gratefully acknow- ledged: DTRC Independent Research Program, sponsored by the Office of the Chief of Naval Research, Director of Navy Laboratories, OCNR Code 300, and administered by the Research Coordinator, DTRC Code 0112 (Dr. Bruce Douglas), under program element 61152N, Task Area R00N0000, under DTRC Work Unit 1-2844-150. This work was per- formed by Codes 644 and 844.

REFERENCES

1. Lakes, R., Science, 235 (1987) 1038. 2. Lakes, R., Proc. 20th Midwestern Mechanics Conf., 1987, pp. 758-62. 3. Andersson, P., Noise and Vibration Control Worldwide, Jan;/Feb., (1981) 16. 4. Bruel & Kjaer, Instruction Manual, Standing Wave Apparatus, Type 4002. 5. Avallone, E. & Baumeister, T., Marks' Standard Handbook for Mechanical

Engineers, 9th ed. McGraw-Hill, New York, USA, 1978, ISBN 0-07-004127-X. 6. Reynolds, D. D., Engineering Principles of Acoustics, Noise and Vibration

Control. Allyn & Bacon, Boston, USA, 1981, ISBN 0-205-07271-6. 7. Weast, R. (ed.), Handbook of Chemistry & Physics, 51 st edn, Chemical Rubber

Co., Cleveland, USA, 1970.