State space solution of the layered axial symmetric problem in piezoelectric,piezomagnetic and elastic media
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In this paper, the methodology is based on a state space formulation where a particular collection of elastic,electric and magnetic variables is used to determine the behavior of a layered transversely isotropic space subjected to piezoelectric,piezomagnetic and elastic media under arbitrary loading conditions. The state vector equation of the transversely isotropic space axial symmetric problem in piezoelectric,piezomagnetic and elastic media is established. By the use of the Hankel integral transform,the state vector equations are transformed into a set of ordinary differential equations. According to the theory of ordinary differential equations and the CaylayHamilton theorem, the solutions of state vector equation are obtained which are the product of initial state variables and transfer matrix. The general formulation of the solution for the multilayer space axial symmetric problem in piezoelectric,piezomagnetic and elastic media is given using the method of transfer matrix.