Asymptotic expansion of the dispersion equation of two-component wave in periodically layered elastic media with initial deformations

Abstract

    The present paper deals with the problem on two-component wave propagation in periodically layered, in the case of long wavelength approximation or the layers are thin. The mediums assumed are incompressible elastic media with initial deformations. This problem is solved by applying asymptotic expansion method. The asymptotic expressions of the displacement, the stress has been established. Wave velocity is a series of powers of small parameter ε = kh, where k is the wave number, h is the thickness of one periodicity cell. The first three coefficients of the series are determined directly. The recurrent formulas are constructed to determine coefficients of higher power.