Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates

An analytical model for free vibration analysis of piezoelectric coupled moderately thick circular plate is presented based on Mindlin’s plate theory for the cases where electrodes on the piezoelectric layers are shortly connected. The distribution of electric potential along the thickness direction is simulated by a sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The detailed mathematical derivations are presented. Numerical investigations are performed for plates with two surface-bonded piezoelectric layers for various diameter–thickness ratios and the results are verified by those obtained from three-dimensional finite element analyses (ABAQUS 6.1