Plane Wave Propagation and Internal Instability in Finely Layered Media

Authors

  • Richard W. Perkins, Jr.
  • Kumar G. Punwani
  • Donald C. Robertson

Abstract

An exact elasticity solution for transverse waves is presented for an infinite periodic layered medium that is subjected to initial stress and that is incrementally elastic. Exact results are compared with various approximate theories. It appears that the microstructure approximate method may be sufficiently accurate to permit use in problems of acoustic propagation and impact loading. Internal instability of the layered medium is treated as a special case of the general dynamic problem.

References

Biot, M. A. 1940. The influence of initial stress on elastic waves. J. Appl. Phys. 11: 522-530.nBiot, M. A. 1963. Internal buckling under initial stress in finite elasticity. Proc. Roy. Soc., Series, A. 273: 306-329.nBiot, M. A. 1965. Mechanics of incremental deformations. John Wiley and Sons.nBiot, M. A. 1967. Rheologieal stability with couple-stresses and its application to geological folding. Proc. Roy. Soc., Series A. 298: 402-423.nBrekhovskikh, L. M. 1960. Waves in layered media. Academic Press.nHermann, G. 1970. Dynamics of composite materials. Page 183 in A. C. Eringen, ed. Recent advances in engineering science, v. 5, Pt. 1. Gordon and Breach.nKiusalaas, J., and W. Jaunzemis. (in press.) Internal buckling of a laminated medium. Presented at the Fifth South Eastern Conference on Theoretical and Applied Mechanics, 1970, to appear in Conference Proceedings.nMindlin, R. D. 1964. Microstructure in linear elasticity. Arch. Ration. Mech. Anal., 16: 57.nPerkins, R. W. 1972. On the mechanical response of materials with cellular and finely layered internal structure. Chapter 5 in B. A. Jayne, ed., Theory and design of wood and fiber composite materials, Syracuse University Press.nRytov, S. M. 1956. Acoustical properties of a thinly laminated medium, Soviet Phys. Acoust., 2: 68-80.nSun, C. T., J. D. Achenbach, and G. Hermann. 1968. Continuum theory for a laminated medium. J. Appl. Mech. 35: 467-475, Sept. 1968.n

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Published

2007-06-05

Issue

Number 4 / Winter 1973

Section

Research Contributions

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