NEW ANALYTICAL METHOD OF DISPERSION CURVES IN PLANE LAYERED STRUCTURES

Abstract

The propagation of sound through plane layered structures is considered, with emphasis on three-layers made up of thick isotropic plates coupled with a thin anisotropic one. Modes are obtained by means of the transition terms method (TTM) based upon the use of the reflection and transmission coefficients. This method differs from the root searching methods (RSM) of dispersion equations such as, for instance, the Newton–Raphson method. The TTM provides dispersion curves with very little computation time. It unifies the dual representation of the dispersion curves: either complex wave numbers versus the real frequency, or complex frequencies versus the real wave number. The application to various cases of three-layer structures allows us to check the validity of the method and to discuss the connection between the TTM and Cremer's correspondence principle.