Thermal Vibration of Functionally Graded Circular Plates

Abstract

Based on the nonlinear theory of von Karman plate, axisymmetric nonlinear vibration of a functionally graded circular plate with clamped boundary condition is investigated under thermal loading. It is assumed that the mechanical and thermal properties of functionally graded materials vary continuously through the thickness of the plate and obey a simple power law related to the volume fraction of the constituents. Motion equations for the problem are derived. Existence of harmonic vibrations is assumed and then Ritz-Kantorovich method is used to convert the dynamic Von Karman equations to a set of nonlinear ordinary differential equations. Finally a shooting method is employed to numerically solve the resulting differential equations. Effects of amplitude A, thermal load parameter λ and material constant n on the vibration behavior of FGM plate are discussed in details.