3D symplectic expansion for piezoelectric media

The symplectic series expansion method is extended to three-dimensional problem for transversely isotropic piezoelectric media. The governing equations are first derived in Hamiltonian form, and symplectic eigensolutions are directly obtained through analytical method. All solutions of the problem are reduced to finding eigenvalues and eigensolutions. The classical St Venant solutions are described by zero-eigensolutions, and the localized solutions are depicted by non-zero-eigensolutions. Symplectic relationships of the ortho-normalization are used, end conditions are rewritten by eigensolutions, and a numerical scheme is formed analytically. Some numerical examples are given. Copyright © 2007 John Wiley & Sons, Ltd.