FREE VIBRATION ANALYSES OF POROUS FGM RECTANGULAR PLATES ON A WINKLER-PASTERNAK ELASTIC FOUNDATION CONSIDERING THE TEMPERATURE EFFECT

Based on the classical thin plate theory and Hamilton principle, the free vibration characteristics of porous functionally graded material (FGM) rectangular plates on a Winkler-Pasternak elastic foundation under the influence of temperature are studied. The Voigt mixed power law model and random distribution model of pores are used to characterize the material properties of porous FGM rectangular plates, and the uniform temperature rise in a porous FGM rectangular plate and the temperature dependency of material properties are considered. The governing differential equation of a porous FGM rectangular plate on the elastic foundation is derived from the physical neutral surface position. The dimensionless form of the governing differential equation is also obtained. The differential transformation method (DTM) is then used to transform the dimensionless governing differential equation and its boundary conditions. Six typical boundaries are introduced and programmed in MATLAB. The calculation accuracy is consistent. After iterative convergence, the dimensionless natural frequencies are solved. The effects of the boundary conditions, gradient index, temperature rise, porosity, aspect ratio, side-to-thickness ratio, dimensionless elastic stiffness coefficient and dimensionless shear stiffness coefficient on the vibration characteristics of FGM rectangular plates are studied by numerical examples.