RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

The random response of a piezoelectric thick shell in plane strain state under bound-axy random excitations is studied and illustrated with a piezoelectric cylindrical shell. The dif-ferential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions axe converted into homogeneous ones by transformation, which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials, which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system axe derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell axe finally obtained, and the frequency-response characteristics and the electrical and mechanical coupling properties arc explored.