The effective finite element method for free and forced vibration analysis of 2D-FGSW plates lying an elastic foundation

The purpose of this study is to analyze the influence of geometric parameters and material properties on the free and forced vibration of bi-directional functionally graded sandwich (2D-FGSW) plates lying on an elastic foundation (EF) using an effective finite element method (FEM) based on the trigonometric shear deformation theory (TrSDT). The mechanical properties of 2D-FGSW are variable in both the x- and z-directions. The EF includes the springer stiffness k1 and the shear layer stiffness k2. Moreover, the impacts of structural damping and periodic loading on the behavior of 2D-FGSW plates are considered. Element matrices are created using a four-node quadrilateral plate element (Q4) with eight degrees of freedom per node. The effectiveness and accuracy of the current formulation are confirmed by contrasting the acquired results with those of earlier works. Then, many studies are carried out to illustrate how input parameters might affect the vibration characteristics of 2D-FGSW plates lying on EF. In addition, the eigenfrequencies of different types of 2D-FGSW plates with a center hole are investigated.