Flexural vibration of a smart laminated FGM plate with initial imperfections

This paper presents a free vibration analysis of a geometrically imperfect, smart FGM laminated plate that is composed of a shear deformable functionally graded layer and two surface-mounted piezoelectric actuator layers. The theoretical formulation is based on Reddy's higher order shear deformation plate theory and includes the effect of a pre-vibration state induced by a temperature change and an applied control voltage. By adding an incremental dynamic state to the pre-vibration state, the governing differential equations are derived for the flexural vibration of imperfect smart FGM laminated plates. A semi-analytical method that makes use of one-dimensional differential quadrature and Galerkin technique is proposed to predict the vibration behavior of laminated rectangular plates with two opposite clamped edges and different initial imperfections. Numerical results are presented in both tabular and graphical forms , showing the influence of imperfection mode, control voltage, out-of-plane boundary support, temperature change, and the side-tothickness ratio on the vibration characteristics of the plate.