A new higher-order shear deformation theory for frequency analysis of functionally graded porous plates

摘要

The current investigation aims to account for the influence of porosity modeling while studying the dynamic response of functionally graded material (FGM) plates within the framework of a new, higher-order shear deformation theory for the first time. In the newly developed porosity modeling, the reciprocal effect of mass density and Young's modulus is considered. Furthermore, silicon carbide in the ceramic phase and nickel in the metallic phase are selected as the constituent materials of the functionally graded plate. Based upon the new higher-order theory, the kinetic and kinematic relations are derived. This theory does not need any shear correction factor. The dynamic form of the principle of virtual work is employed to achieve governing equations of structure. Afterward, Galerkin's method is implemented to solve obtained governing equations of porous, functionally graded plates. In order to verify the accuracy of the method, the obtained results were compared with the results reported in the literature, and good agreement was found. At last, the influences of some parameters such as porosity coefficient, length to thickness ratio, and aspect ratio of the porous, FGM plate on the dimensionless frequency are studied and the results are illustrated in detail.