Evaluation of complex spectrum of the symmetrical Lamb waves for three-layered plates at low frequency. Part I: Foundations

摘要

A new method combining the asymptotic and iteration approaches to study the total wavenumber spectrum for a plate made of isotropic layers is suggested. In this part we use the propagator matrices to deduce the dispersion equation and its static limit in a closed form with the use of symbolic calculations. The roots in statics which are analyzed at the first step play the key role. Then, the low frequency approximations for the dispersion curves are derived. The method is aimed to evaluate a dispersion curve of any order n and to describe it in a closed form by an asymptotic formula. Especially it concerns the case n -> +infinity which causes difficulty for the pure numerical approaches.