Thermal Behavior Analysis at Large Free Vibration Amplitudes of Thin Annular FGM Plates with Porosities

Geometrically nonlinear free vibration of Functionally Graded thin Annular Plates (FGAP) with porosities subjected to thermal environment is investigated. A semi-analytical model based on an extension of the Rayleigh Ritz method to nonlinear vibrations is considered. A homogenization procedure has been employed to reduce the problem to that of an isotropic homogeneous annular plate. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The rule of mixture has been modified in order to take into account the effect of porosity and approximate the material properties. The problem is solved by a numerical iterative method. The effects of the porosity volume fraction, the temperature distribution through the plate thickness and temperature-dependency of material properties on the nonlinear free vibrations responses of the FGAP at large amplitudes are examined and discussed in detail.