Nonlinear vibration of functionally graded cylindrical shells embedded with a piezoelectric layer

This paper addresses the nonlinear vibration problem of simply supported functionally graded (FG) cylindrical shells with embedded piezoelectric layers. The governing differential equations of motion of the FG cylindrical shell are derived using the Lagrange equations under the assumption of the Donnell׳s nonlinear shallow-shell theory. A semi analytical approach, wherein the displacement fields are expanded by means of a double mixed series based on linear mode shape functions for the longitudinal, circumferential and radial variables, is proposed to characterize the nonlinear response of the cylindrical shell. The large-amplitude response and amplitude frequency curves of the cylindrical shell are obtained by using the proposed approach. Finally, the effects of excitation force and applied voltage on the vibration behavior of the cylindrical shell are investigated.