Floquet waves in anisotropic periodically layered composites

The field equations governing the plane harmonic elastic motions of anisotropic stratified media are written in the form of a matrix system of differential equations, where the dependent variables are the displacements and tractions acting across planes normal to the direction of stratification. In the case of periodically layered media, Floquet’s theorem and the propagator matrix method can be applied to solve the governing sextic matrix equation. In the absence of sources or body forces, the general motion of the layered medium is described by a combination of six partial waves (Floquet waves). A closed-form algebraic solution for the dispersion equation of such waves is derived. Numerical results describing the dispersion spectrum of a cross-ply periodic laminated are discussed in detail.