Nonlinear free vibration analysis of functionally graded plate resting on elastic foundation in thermal environment using higher-order shear deformation theory

Abstract

This paper deals with nonlinear vibration analysis of a functionally graded plate resting on Pasternak elastic foundation in a thermal environment. A mathematical model is developed based on a higher-order shear deformation theory using Green-Lagrange type nonlinearity. The model includes all the nonlinear terms to obtain a general form and to present the original fiexure of the plate. The material properties are considered as temperature dependent and graded along thickness direction following a simple power law distribution in terms of volume fraction of the constituents. The compression/traction free condition is employed to obtain a simplified model with seven parameters instead of nine parameters. The plate model has been discretized into C0 eight-noded quadratic elements with seven degrees of freedom per node. The governing equation of the functionally graded plate has been derived using Hamilton's principle and solved by a direct iterative method. The present model is validated by comparing the obtained results with those published in the literature. The efiects of volume fraction index, aspect ratio, thickness ratio, support conditions, elastic foundation modulus, and temperature on the nonlinear frequencies of the functionally graded plates are discussed. It has been found that the intermediate material property does not necessarily give intermediate nonlinear frequency.