A symplectic eigensolution method in transversely isotropic piezoelectric cylindrical media
XU Xin-sheng, GU Qian, LEUNG Andrew Y. T., ZHENG Jian-jun
State Key Laboratory of Structure Analysis of Industrial Equipment and Department of Engineering Mechanics, Dalian University of Technology, Dalian 116024, China; Department of Building and Construction, City University of Hong Kong, Hong Kong, China
Abstract This paper reports establishment of a symplectic system and introduces a 3D sub-symplectic structure for transversely isotropic piezoelectric media. A complete space of eigensolutions is obtained directly. Thus all solutions of the problem are reduced to finding eigenvalues and eigensolutions, which include zero-eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian matrix and non-zero-eigenvalue solutions. The classical solutions are described by zero-eigensolutions and non-zero-eigensolutions show localized solutions. Numerical results show some rules of non-zero-eigenvalue and their eigensolutions.
