Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory

• Free vibration analysis of FG plate with piezoelectric layers is presented.
• The four-variable refined plate theory is employed.
• Equations of motion are derived using Hamilton׳s principle and Maxwell׳s equation.
• Navier solution is employed for simply supported rectangular plates.
• Simplicity, accuracy and efficiency of presented formulations are proved.

This study presents an analytical solution for free vibration analysis of a functionally graded (FG) plate integrated with piezoelectric layers using four-variable refined plate theory. Equations of motion for simply supported rectangular plates are derived using Hamilton׳s principle and Maxwell׳s equation, and Navier method is employed for solution of equations. The numerical results are presented for isotropic, transversely isotropic and FG plates integrated with piezoelectric layers. The obtained natural frequencies for different examples are compared with the results of other common plate theories. The results demonstrate the simplicity, accuracy and efficiency of presented formulation in vibration analysis of investigated problems.