Dynamic analysis of a rectangular porous plate resting on an elastic foundation using high-order shear deformation theory

Abstract

This research deals with the dynamic analysis of a rectangular plate made of porous materials. The porous plate is subjected to a dynamic transverse load and is resting on a Pasternak foundation. Linear poroelasticity theory is used to obtain the Biot formulation of the constitutive equations for the porous material. Also, the Young modulus and density of the porous plate vary in the transverse direction versus the porosity of the plate. Tennessee marble is the porous material that used in this paper. Reddy’s third-order shear deformation theory with five unknowns, the energy method, and Hamilton’s principle are applied to derive the equations of motion of the porous plate. These equations are solved by a differential quadrature method as a numerical method due to five coupled large equations. A detailed numerical study indicates the significant effects of aspect ratio, thickness ratio, boundary conditions, elastic medium, load intensity, and porosity on deflection of the porous plate. Results of this study can be useful to design of pneumatic conveying, handling, and control systems.

Finite element formulation of metal foam microbeams via modified strain gradient theory

“…Navier solutions based on the stability analysis are provided for the simply support sandwich plate with metal foam core [17]. Differential quadrature technique is implemented to obtain the numerical results for the free vibrations of the third order shear deformable metal foam plate [18].…”

Influence of porosity on the analysis of sandwich plates FGM using of high order shear-deformation theory.

“…Based on the open literature, it seems that many investigators have paid attention to the analysis of FGM structures with porosities. Most of these investigations are concerned with the vibration behavior of FG porous structures [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. The objective of this article is to present the static of bending behavior of sandwich plates FGM having porosities.…”