Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation

An exact solution of nonlinear temperature distribution for free vibration of simply supported functionally graded sandwich plates resting on elastic foundation is presented. Material properties and thermal expansion coefficient of FGM layers are assumed to be temperature-dependent and vary continuously through-the-thickness according to a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on the third-order shear deformation plate theory of Reddy and Hamilton's principle, which includes thermal effects. The thermal loads are assumed to be uniform, linear and nonlinear distribution through-the-thickness. The elastic foundation is modeled as Winkler, Pasternak or Kerr foundation. Various numerical results including the effect of the thermal loading conditions, gradient index, foundation parameters and the mode shape on the nondimensional frequency of FGM sandwich plates are presented.