Calculation of reflection and transmission coefficients for waves in multilayered piezoelectric structures using the mixed variable method.

Abstract

The reflection and transmission (R/T) behavior of elastic waves in an anisotropic multilayered piezoelectric structure bounded by two homogeneous half-spaces is studied using the mixed variable method. The mixed variable method, which is based on the mixed energy matrix, takes the displacement vector at one end of the structure and the stress vector at other end of the structure as the basic variables. The wave equation for a homogeneous piezoelectric layer is transformed into a first-order state equation in the Hamiltonian system by introducing a dual vector. The general solution of the state equation can be expressed in terms of the eigenvalues and eigenvectors of the complex Hamiltonian matrix. A mixed energy matrix is applied to establish the relationship between the generalized displacement and stress vectors on the upper and lower interfaces of a layer. By an efficient recursive algorithm, the global mixed energy matrix is formed for an arbitrarily anisotropic multilayered piezoelectric structure. The R/T coefficients of the waves in an anisotropic multilayered piezoelectric structure are derived by the global mixed energy matrix. Numerical examples are provided to show the robustness of the mixed variable method. The effects of the incident angles, wavenumbers, and critical angles on the R/T coefficients are discussed.