Axisymmetric thermal vibration analysis of graded porous circular plates based on physical neutral surface and Reddy’s third-order shear theory

Abstract

In this article, the free vibration of functionally graded porous (FGP) circular plate with various boundary conditions are investigated by means of the differential quadrature method (DQM) based on Reddy’s theory. Performance of the materials varies continuously in the whole thickness and two cosine forms of nonuniform porosity distribution along its thickness are considered. Hamilton’s principle is adopted to derive the governing equation of the system, which effectively considers the effects of thermal stress. It is worth noting that due to the introduction of physics neutral surface, reducing stretching-bending coupling effect, so the complex governing equations have been appropriately simplified. Then, using the DQ method, the natural frequencies of free vibration of FGP circular plates subjected to thermal environments with various boundary conditions were obtained. Convergence and comparative research are performed to prove the convergence, reliability, and accuracy of the DQ method. The effects of various factors such as porosity coefficient, porosity distribution pattern, temperature rise, thickness-diameter ratio, and boundary conditions on the natural frequencies are discussed in detail.