The effect of visco-Pasternak foundation on the free vibration behavior of exponentially graded sandwich plates with various boundary conditions

In this investigation, an improved integral trigonometric shear deformation theory is employed to examine the vibrational behavior of the functionally graded (FG) sandwich plates resting on visco-Pasternak foundations. The studied structure is modelled with only four unknowns' variables displacements functions. The simplicity of the developed model being in the reduced number of variables which was made with the help of the use of the indeterminate integral in the formulation. The current kinematic takes into consideration the shear deformation effect and does not require any shear correction factors as used in the first shear deformation theory. The equations of motion are determined from Hamilton's principle with including the effect of the reaction of the visco-Pasternak's foundation. A Galerkin technique is proposed to solve the differentials governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for various clamped and simply supported FG sandwich plates resting on visco-Pasternak foundations. The validity of proposed model is checked with others solutions found in the literature. Parametric studies are performed to illustrate the impact of various parameters as plate dimension, layer thickness ratio, inhomogeneity index, damping coefficient, vibrational mode and elastic foundation on the vibrational behavior of the FG sandwich plates.