An accurate method for guided wave propagation in multilayered anisotropic piezoelectric structures

The purpose of this paper is to extend and generalize the precise integration method (PIM) and the Wittrick–Williams (W–W) algorithm to analyze the dispersion of guided waves in multilayered anisotropic piezoelectric structures. The analysis shows that the W–W algorithm cannot be directly applied to piezoelectric materials. This is due to the fact that a submatrix of the Hamiltonian matrix is not positive definite for piezoelectric materials such that the eigenvalue count of sublayers is not zero when the divided sublayers are sufficiently small. The reason for this issue is explored by a theoretical analysis, and then, a symplectic transformation is introduced to ensure that the W–W algorithm can conveniently be applied to solve wave propagation problems in multilayered anisotropic piezoelectric structures. The present method not only guarantees that the computation is accurate and stable, but also finds all eigenfrequencies without being missed. Three numerical examples are provided to illustrate the performance of the method, and the results obtained by the method are compared with the published results and the results obtained by the semi-analytical finite element method. The effects of boundary conditions, wave propagation direction, thickness ratios and stacking sequences on the dispersion behavior of guided waves are discussed.