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Journal of Engineering
Volume 2017, Article ID 1474916, 13 pages
Research Article

Free Vibration of Embedded Porous Plate Using Third-Order Shear Deformation and Poroelasticity Theories

Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

Correspondence should be addressed to Ali Ghorbanpour Arani;

Received 21 July 2016; Revised 17 October 2016; Accepted 7 November 2016; Published 24 January 2017

Academic Editor: Francis T. K. Au

Copyright © 2017 Ali Ghorbanpour Arani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This research aims at studying free vibration of rectangular plate made of porous materials in which Y-foam, G-foam, and 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.