The effect of parameters of visco-Pasternak foundation on the vibration characteristic of a FG square plate integrated with FGP layers

The present paper investigates vibration analysis of a functionally graded square plate integrated with two functionally graded piezoelectric layers as sensor or actuator resting on the elastic Visco-Pasternak foundation. All the mechanical and electrical properties except Poisson’s ratio can vary continuously and gradually along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. Short circuited boundary conditions are considered on the top and bottom of functionally graded piezoelectric layers. The general constitutive relations in electromechanical systems are used for considering the effect of all mechanical and visco-Pasternak foundation parameters. These parameters are including the non-homogeneous indexes of core and piezoelectric layers, direct, shear and damping parameters of foundation. The obtained results present the effect of various mechanical and foundation parameters on the vibration responses of the system. The functionalities of two considered layers and core can be regarded independently and the effect of these indexes can be considered on the responses. The obtained results indicate that with increasing the non-homogeneous index of core and layers, the natural frequencies of the system decreases.