Free vibration analysis of FG plate with piezoelectric layers on elastic foundation using refined shear deformation theory

This study presents an analytical solution for free vibration analysis of functionally graded (FG) core integrated with piezoelectric layers and resting on elastic foundation. The four-variable refined plate theory is utilized which predicts parabolic variation of transverse shear stresses across the plate thickness, satisfies the zero traction on the plate surfaces and does not need the shear correction factor. Using both Hamilton's principle and Maxwell equation, the Equations of motions for simply supported rectangular plates resting on elastic foundation are obtained and the Navier method is adopted for solution of equations. Natural frequencies for different examples are obtained and they are compared with other common plate theories. It can be concluded that besides the simplicity of the presented formulation, this theory which does not need for shear correction factor, is very accurate in analysis of plates integrated with piezoelectric layers resting on elastic foundation and is comparable to other theories (the first order shear deformation theory (FSDT) and third order shear deformation theory). Also effects of power law index, thickness ratio and foundation parameter, on the natural frequency of plates have been investigated.