On natural frequencies of Levy-type thick porous-cellular plates surrounded by piezoelectric layers

In this paper, an analytical solution for free vibration of rectangular porous-cellular plates enclosed by piezoelectric layers is presented by using third-order shear deformation plate theory. Using Hamilton's principle and Maxwell equation, the governing equations of the system are obtained for both closed and open circuit conditions. Due to the coordinate dependency of mechanical properties of porous materials, the governing equations of motion are highly coupled. By using four auxiliary functions, these equations convert into two independent partial differential equations. The decoupled equations are solved analytically by employing Levy-type boundary conditions for the plate. Finally, after validation of the obtained results, the effects of various parameters such as porosity and geometrical dimensions on the natural frequencies of plate are investigated for different electrical and mechanical boundary conditions. It is found that the natural frequencies of the plate decrease as the coefficient of plate porosity increases. Also, the piezoelectric layers cause the natural frequency of the plate to increase in various vibrating modes.