Stochastic response analysis of piezoelectric axisymmetric hollow cylinders

The stochastic response of a piezoelectric thick axisymmetric hollow cylinder in plane strain under boundary stochastic excitations is analyzed and calculated. The stochastic stress and electric-potential boundary conditions of the piezoelectric hollow cylinder are converted into homogeneous boundary conditions by transformations that yields the electrical and mechanical coupling partial differential equations of motion with damping and stochastic excitations. The equation for electric potential is integrated radially to obtain the electric potential as a function of displacement, and the displacement is expanded as a series in terms of the Legendre polynomials. The partial differential equation for displacement is further converted into ordinary differential equations by using the Galerkin method, which represent a stochastic multi-degree-of-freedom system with asymmetric stiffness matrix due to the asymmetric electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and correlation function matrix of the system response are derived from these equations based on the theory of random vibration. The expressions of mean-square displacement and electric potential of the piezoelectric hollow cylinder are finally obtained and illustrated by numerical results for non-white stochastic excitations. The frequency-response characteristics and electrical and mechanical coupling properties are explored.