Nonlinear dynamic analysis of viscoelastic FGM with linear and nonlinear porosity distributions

This paper investigates the dynamic analysis of Viscoelastic Porous Functional Graded Material (VPFGM) plates under constant and variable loading versus time. The material properties of VPFGM plates are obtained from the power-law P-FGM that governs the variation of the material, through the thickness of the plate. New forms of porosity distribution have been studied by considering uniform, linear and non-linear distributions. Hamilton's principle is used in deriving the governing equations of motion. Then, a variational formulation based on Third-order Shear Deformation Theory (TSDT) is used. And after, the obtained equations are resolved numerically by the Finite Element Method (FEM) by adopting four node quadrilateral element with 7 Degrees Of Freedom (DOF) per node. The obtained results were compared with other approaches to demonstrate the effectiveness and performance of the proposed approach. The numerical results showed that this present approach can solve the problem with high accuracy and efficiency. Our results are in parallel with those from the literature. New finding, compared to the literature, were investigated for VPFGM. The analysis shows that damping ratios and the volume fraction of the P-FGM and that of the porosity have a significant effect on the dynamic behavior of VPFGM plates.