Dynamics of anisotropic multilayers

A formalism is developed for the description of elastic wave propagation in an arbitrarily layered plate (piece-wise homogeneous or continuously inhomogeneous) of unrestricted anisotropy. The analysis is based on the propagator matrix approach. The boundary-value problems of the plate with free, clamped or free/clamped faces are formulated and reduced to real dispersion equations. These equations are analyzed in the long- and short-wavelength limits. It is proved that three fundamental wave branches always exist in an arbitrary layered plate with free faces. And a plate, which has at least one clamped surface, in principle, cannot carry fundamental waves. On the contrary, a wave-guide part of the plate spectrum exists for all considered types of boundary conditions. The found high-frequency asymptotics of dispersion curves relate to three kinds of eigenwaves: localized modes at surfaces and interfaces (Rayleigh- and Stoneley-type modes) and bulk wave-guided modes.