Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method

Abstract

The objective of the present paper is to study the effect of porosity on vibration and buckling responses for sandwich plate supported with different boundary conditions at the edges. The formulation is performed for recently developed sandwich plate using new modified sigmoid function based functionally graded material plate of different symmetric and asymmetric configurations. Three different types of porosity are considered viz. even, uneven but symmetric, and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The variational principle is employed to derive equilibrium equations. A closed form solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions using Galerkin Vlasov’s method. Free vibration and buckling analysis have been performed to study the effect of porosity, geometric configurations, inhomogeneity parameter, and buckling load parameter. These studies are performed on sandwich sigmoid function based functionally graded material plate for different boundary conditions and plate configurations. It is observed that in several cases with uneven symmetric porosity (P-2) distribution, the reduction in effective inertia appears to be more prominent in comparison to the reduction in effective stiffness of the plate and uneven non-symmetric porosity (P-3) distribution ascertains the realistic idealization for a plate with micro-voids. The higher modes of vibrations and nature of in-plane load are very sensitive to the type of porosity distribution considered. In addition, zero frequency parameter and zero critical buckling load in a load frequency curves correspond to critical buckling load and frequency parameter, respectively. The accuracy and validation of the present formulation are determined by considering different examples.