Abstract:Based on the first-order shear deformation theory， the free vibration characteristics of a circular plate of porous Functionally Gradient Material （FGM） on an elastic foundation in a thermal environment are studied. First， Voigt modified mixed power law model with pores is considered， and a unified temperature field is given to describe the temperature dependence of materials. Using Hamilton’s principle， the governing differential equation of free vibration of porous FGM circular plate on elastic foundation under thermal environment is derived and dimensionless. Then the dimensionless governing differential equation and boundary conditions are transformed by using the differential transformation method， and the algebraic characteristic equations for dimensionless natural frequencies and critical temperature rise are obtained. The problem is degenerated and compared with the existing literature results to verify its effectiveness. Finally， the influence of gradient index， porosity， boundary conditions， thickness radius ratio， temperature rise， and Winkler elastic foundation coefficient on the dimensionless natural frequency of porous FGM circular plate as well as the influence of relevant parameters on the critical temperature rise is calculated and analyzed. The results show that the gradient index affects the frequency， reflecting the characteristics of the transition of materials from ceramics to metals. Porosity weakens the stiffness and then affects the natural frequency. Winkler foundation has a role in strengthening the stiffness， and the increase in temperature causes thermal buckling and instability of the structure.