Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments

A large amplitude vibration analysis is presented for a shear deformable doubly curved panel made of functionally graded materials (FGMs) resting on elastic foundations in thermal environments. The effective material properties are evaluated using the Mori-Tanaka micromechanics model. The formulations are based on a higher order shear deformation theory and von Kármán strain-displacement relationships. The panel-foundation interaction and thermal effects are also included. The temperature-dependent material properties of FGMs are assumed to be graded in the thickness direction according to a simple power law distribution. The motion equations are solved by a two-step perturbation approach to determine the nonlinear frequencies of the FGM doubly curved panel. The numerical illustrations cover small- and large-amplitude vibration characteristics of FGM doubly curved panels resting on elastic foundations of Pasternak-type. The results obtained from the Mori-Tanaka model are compared with those obtained from the Voigt model. The results confirm that in most cases Voigt model and Mori-Tanaka model have the same accuracy for predicting the vibration characteristics of FGM doubly curved panels. The effects of volume fraction index, temperature variation, foundation stiffness and panel curvature ratio on the nonlinear free vibration behaviors of FGM doubly curved panels are also discussed in detail.