Harmonic wave propagation in composite materials

Abstract

This paper presents a study of the propagation of harmonic waves of plane strain in elastic composite materials. The composite structure is idealized as an assembly of identical subregions, each with the displacement field represented by a finite number of generalized displacements. The resulting model possesses a periodic lattice-type structure and its response to harmonic waves can be investigated as a problem in lattice dynamics. A set of generalized coordinates, applicable for the case of harmonic wave propagation in the discrete periodic structure, is employed to generate an algebraic eigenvalue problem, the solution of which gives the frequency spectrum for the medium. To show the accuracy of this method, examples of harmonic wave propagation in infinite isotropic and orthotropic homogeneous plates are presented, and cases of harmonic wave propagation in infinite isotropic and orthotropic media. The method is used to generate the frequency spectra for both a fiber-reinforced composite plate and an infinite composite medium to clearly indicate the dispersive effects which exist in periodic media when the half wavelength–lattice dimension ratio approaches unity. These results are compared with several well-known theories for composite materials. Subject Classification: 20.15.