Abstract
Propagation of time-harmonic elastic waves through periodically inhomogeneous media is considered. The material inhomogeneity exists in a single direction along which the elastic waves propagate. Within the period of the linear elastic and isotropic medium, the density and elastic modulus vary either in a continuous or a discontinuous manner. The continuous variations are approximated by staircase functions so that the generic problem at hand is the propagation of elastic waves in a medium whose finite period consists of an arbitrary number of different homogeneous layers. A dynamic elasticity formulation is followed and the exact phase velocity is derived explicitly as a solution in closed form in terms of frequency and layer properties. Numerical examples are then presented for several inhomogeneous structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M.; Stegun, I. (eds) (1972): Handbook of mathematical functions. Dover Publ., New York, pp. 504–505
Bedford, A.; Drumheller, D. S.; Sutherland, H. J. (1976): On modeling the dynamics of composite materials. In: Nemat-Nasser, S. (ed): Mechanics Today 3, 1–54
Behrens, E. (1967): Sound propagation in lamellar composite materials and averaged elastic constants. J. Acoust. Soc. Am. 42/2, 378–383
Brillouin, L. (1953): Wave propagation in periodic structures. 2nd ed. New York: Dover Publications
Christensen, R. M. (1979): Mechanics of composite materials. New York: Wiley
Delph, T. J.; Herrmann, G.; Kaul, R. K. (1978): Harmonic wave propagation in a periodically layered, infinite elastic body: antiplane strain. ASME J. Appl. Mech. 45, 343–349
Delph, T. J.; Herrmann, G.; Kaul, R. K. (1979): Harmonic wave propagation in a periodically layered, infinite elastic body: plane strain, analytical results. ASME J. Appl. Mech. 46, 113–119
Kohn, W.; Krumhansl, J. A.; Lee, E. H. (1972): Variational methods for dispersion relations and elastic properties of composite materials. ASME J. Appl. Mech. 39, 327–336
Lee, E. H.; Yang, W. H. (1973): On wave in composite materials with periodic structure. SIAM J. Appl. Math. 25, 492–499
Mal, A. K. (1988): Guided waves in layered solids with interface cones. Int. J. Eng. Sci. 26, 873–881
Nemat-Nasser, S.; Fu, F. C. L. (1974): Harmonic waves in layered composites: bounds on frequencies. ASME J. Appl. Mech. 41, 288–290
Nemat-Nasser, S.; Yamada, M. (1981): Harmonic wave in layered transversely isotropic composites. J. Sound and Vibration 79, 161–170
Robinson, C. W.; Leppelmeier, G. W. (1974): Experimental verification of dispersion relations for layered composites. ASME J. Appl. Mech. 41, 89–91
Rytov, S. M. (1965): Acoustical properties of a thinly laminated medium. Soviet Physics Acoustic 2, 68–80
Shah, A. H.; Datta, S. K. (1982): Harmonic waves in a periodically laminated medium. Int. J. Solids Struct. 18, 397–410
Sve, C. (1971): Time-harmonic wave traveling obliquely in a periodically laminated medium. ASME. J. Appl. Mech. 38, 477–482
Tauchert, T. R.; guzelsu, A. N. (1972): An experimental study of dispersion of stress waves in a fiber-reinforced composite. ASME J. Appl. Mech. 39, 98–102
Ziegler, F. (1977): Wave propagation in periodic and disordered layered composite elastic materials. Int. J. Solids Struct. 13, 293–305
Author information
Authors and Affiliations
Additional information
Communicated by D. E. Beskos, December 11, 1992
Rights and permissions
About this article
Cite this article
Sotiropoulos, D.A. Dispersion of elastic waves in periodically inhomogeneous media. Computational Mechanics 12, 134–146 (1993). https://doi.org/10.1007/BF00371989
Issue Date:
DOI: https://doi.org/10.1007/BF00371989