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

Abstract

This research aims at studying free vibration of rectangular plate made of porous materials in which Y -foam, G -foam, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>C</mml:mi><mml:mi>o</mml:mi><mml:mi>u</mml:mi><mml:mi>s</mml:mi><mml:mi>t</mml:mi><mml:mi>o</mml:mi><mml:mi>n</mml:mi><mml:mi>e</mml:mi></mml:math>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.