Explicit expressions of eigenvalues and eigenvectors for transversely isotropic piezoelectric materials

Explicit expressions of eigenvalues and associated eigenvectors in Stroh's theory [1] for transversely isotropic piezoelectric materials under generalized plane deformation are presented. It is shown that the practical calculation for some piezoelectric ceramics yields all eigenvalues which are distinct from each other for generalized x-z plane deformation, where z is the poling axis of a transversely isotropic piezoelectric material. Some numerical results based on the explicit expressions are given, and the orthogonality and closed relation between matrices A and B in Stroh's theory [2], [3] for piezoelectric material are verified numerically.