Asymptotic expansion of the dispersion equation of Lamb waves in periodically layered elastic media

Abstract

The present paper deals with the problem on Lamb waves propagation in periodically layered, compressible elastic media with initial deformations, in the case of long wavelength approximation (i.e. E = k.h < < 1, where k is the wave number, h is the thickness of one periodicity cell). With the assumption that E < < 1, the dispersion equation is written as: 2 = 2 = [h + c!"h + c2D3 + ... = L cmDm+l·m=0. The main aim of this paper is to find formulae for determining the coefficients Di, ( i 2'. 1). In particular, we prove that D2n = 0 (n 2'. 1), derive formulae for D1 , D3, and construct recurrent formulae for D2n+i (n 2'. 2). Based on these formulae, the solution with any order of accuracy can be obtained. This research is an extension of the investigation by Norris and Santosa [Norris A. and Santosa F., Wave Motion 16 (1992), 33-55] from SH waves (one-component waves) to Lamb waves (two-component waves).