Nonlinear vibration and dynamic response of functionally graded plates in thermal environments

Abstract

This paper deals with the nonlinear vibration and dynamic response of functionally graded material plates in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on the higher-order shear deformation plate theory and general von Kármán-type equation, which includes thermal effects. All four edges of the plates are assumed to be simply supported with no in-plane displacements. The equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of functionally graded plates. The numerical illustrations concern nonlinear vibration characteristics of functional graded plates with two constituent materials in thermal environments. The results reveal that the temperature field and volume fraction distribution have significant effect on the nonlinear vibration and dynamic response of the functionally graded plate.