Simulation and Numerical Analysis of the Effect of Proelastic Composite Material on the Vibration Behavior of Rectangular Plate

In this research, the free vibration of poroelastic composite rectangular plates has been investigated considering Biot's theory of proelasticity and based on modified shear deformation theories. The governing equations of the vibration behavior of poroelastic composite rectangular plate are solved using the Galerkin method and with the help of Mathematica software, which results in obtaining dimensionless natural frequencies and the shape of vibration modes for poroelastic composite rectangular plates. In this study, modified theories of exponential, trigonometric, hyperbolic, parabolic and two high-order shear deformation theories have been used to approximate plate displacements, in which the effect of rotational inertia and transverse shear deformation have been considered. Biot's theory of poroelasticity has also been used to describe the relations governing poroelastic materials. The theories used in this study do not have the shortcomings of classical theories, and hence improve the static and dynamic responses. The innovation of the current study is the use of the theory of poroelasticity based on the theory of modified shear deformation and the solution of the governing equations using the Galerkin method. Three non-uniform symmetric, non-uniform asymmetric and uniform distributions are considered for porosity modeling and poroelasticity theory is used to investigate fluid behavior inside cavities. Also, the influences of different parameters including porosity coefficient, Biot’s effective stress coefficient, Skempton coefficient and length-to-width ratio have been investigated. To check the accuracy of the method used in this research, the numerical results were compared with the results in the references.