Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment

This paper deals with the small- and large-amplitude vibrations of compressively and thermally post-buckled sandwich plates with functionally graded material (FGM) face sheets in thermal environments. Both heat conduction and temperature-dependent material properties are taken into account. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents, and the material properties of both FGM face sheets and a homogeneous substrate are assumed to be temperature dependent. The formulations are based on a higher-order shear deformation plate theory and a general von Kármán-type equation that includes a thermal effect. The equations of motion are solved by an improved perturbation technique. The numerical illustrations concern small- and large-amplitude vibration characteristics of post-buckled sandwich plates with FGM face sheets under uniform and non-uniform temperature fields. The results show that, as the volume fraction index increases, the fundamental frequency increases in the pre-buckling region, but decreases in the post-buckling region. In contrast, the nonlinear frequency ratio decreases in both the pre- and post-buckling region on increasing the volume fraction index. The results also reveal that the substrate-to-face sheet thickness ratio and temperature changes have a significant effect on the fundamental frequency, but only have a small effect on the nonlinear frequency ratio.