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This research aims at studying free vibration of rectangular plate made of porous materials in which Y-foam, G-foam, and Coustone are used and compared with each other. To obtain the Biot formulation of the constitutive equations for a porous material, linear poroelasticity theory is used. Young modulus and density of porous plate are different in transverse direction versus porosity. In order to increase the accuracy of results in comparison with classical plate and first-order shear deformation theories, Reddy’s theory was utilized in this research. Besides, five coupled equations of motion have been studied using Hamilton’s principle and are solved by differential quadrature method (DQM). Detailed results of this study show the significant effect of aspect ratio, thickness ratio, boundary conditions, and porosity on dimensionless frequency and deflection of porous plate. Results of this study can contribute to the design of pneumatic conveying, handling, and control systems.

In this paper, a numerical algorithm using a coupled finite element-differential quadrature (DQ) method is proposed for the dynamic analysis of laminated composite coated beams subjected to a stream of accelerating oscillators. The finite element method with cubic Hermitian interpolation functions is used to discretize the spatial domain. The DQ method is then employed to discretize the time domain. The resulting set of algebraic equations can be solved by either direct methods or iterative methods. It is revealed that the DQ method stands out in numerical accuracy, as well as in computational efficiency, over the well-known standard finite difference schemes, such as the Newmark, Wilson θ, Houbolt, and central difference methods, for the cases considered. Furthermore, in the numerical examples, the effects of various parameters having something to do with the title problem, such as lamina thickness, orientation of the coats, arrival time intervals, velocities, and accelerations of the oscillators on the dynamic behavior of the system, are investigated. The technique presented in this investigation is general and can be easily applied to any time-dependent problem.

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.