Free Wave Propagation in Plates of General Anisotropic Media

Abstract

We develop the analysis for the propagation of free waves in a general anisotropic plate. We begin with a formal analysis of waves in a plate belonging to the triclinic symmetry group. The calculation is then carried forward for the slightly more specialized case of a monoclinic plate. We derive the secular equation for this case in closed form and isolate the mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms. Material systems of higher symmetry, such as orthotropic, transversely isotropic, cubic, and isotropic are contained implicitly in our analysis. We also demonstrate that the particle motions for Lamb and SH modes uncouple if propagation occurs along an in-plane axis of symmetry. We present numerical free-wave dispersion results drawn from concrete examples of materials belonging to several of these symmetry groups.