Both conventional and negative Poisson ’s ratio foams exhibit dispersion of acoustic waves, as well as cut-off frequencies, at which the group velocity tends to zero. This macroscopic behavior is attributed to micro-vibration of the foam cell ribs. The purpose of this article is to develop a micromechanical model of the cut-off frequency. This model is based on the resonance of ribs which may be straight, curved, or convoluted. As foam cell ribs become more curved, the cut-off frequency decreases. Therefore foams with curved or convoluted ribs are expected to provide superior performance in applications involving the absorption of sound.
Issue Section:
Technical Papers
1.
Sutherland
H. J.
Dispersion of Acoustic Waves by Fiber-Reinforced Viscoelastic Materials
,” J. Acoust. Soc. Am.
, Vol. 57
, pp. 870
–875
(1975
).2.
Kinra
V. K.
Ker
E.
Datta
S. K.
Influence of Particle Resonance on Wave Propagation in a Random Particulate Composite
,” Mechanics Research Communications
, Vol. 9
(2
), pp. 109
–114
(1982
).3.
Lakes
R. S.
Size Effects and Micromechanics of a Porous Solid
,” J. Materials Sci.
, Vol. 18
, pp. 2572
–2580
(1983
).4.
Chen
C. P.
Lakes
R. S.
Dynamic Wave Dispersion and Loss Properties of Conventional and Negative Poisson’s Ratio Polymeric Cellular Materials
,” Cellular Polymers
, Vol. 8
, pp. 343
–359
(1989
).5.
Lakes
R. S.
Foam Structures with a Negative Poisson’s Ratio
,” Science
, Vol. 235
, pp. 1038
–1040
(1987
).6.
Howell, B., Prendergast, P., and Hansen, L., “Acoustic behavior of negative Poisson’s ratio materials,” DTRC-SME-91/01, David Taylor Research Center, Mar. 1991.
7.
Christensen, R. M., Theory of Viscoelasticity, 2nd ed., p. 48-New York, Academic Press, 1982.
8.
Eringen, A. C., “Theory of Micropolar Elasticity,” Fracture, Vol. 1, p. 621, Liebowitz, H., ed., Academic Press, 1968.
9.
Mindlin
R. D.
Microstructure in Linear Elasticity
,” Archive for Rational Mechanics and Analysis
, Vol. 16
, pp. 51
–78
(1964
).10.
Harris, C. M., and Crede, C. E., Shock and Vibration Handbook, 2nd ed., p. 7–36, New York, McGraw-Hill, 1976.
11.
Ashby
M. F.
The Mechanical Properties of Cellular Solids
,” Metallurgical Transactions A
, Vol. 14A
, pp. 1755
–1769
(1983
).12.
Gibson, L. J., and Ashby, M. F., Cellular Solids, Pergamon, Oxford, 1988.
13.
Hartog, D., Mechanical Vibrations, 4th ed., p. 167, New York, McGraw-Hill, 1956.
14.
Doughtie, V. L., and Vallance, A., Design of Machine Members, 4th ed., p. 312, New York, McGraw-Hill, 1964.
15.
Ferry, J. D., Viscoelastic Properties of Polymers, 3rd ed., p. 159, New York, Wiley, 1970.
16.
Smith, R. A., Wave Mechanics of Crystalline Solids, Chapman and Hall, London, 2nd ed., 1969.
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