Large amplitude vibration of FGM plates in thermal environment subjected to simultaneously static pressure and harmonic force using multimodal FEM

A nonlinear finite element modeling is proposed to study the dynamic response of functionally graded material (FGM) plates subjected simultaneously to thermal, static, and harmonic loads. The material properties depended on the temperature are assumed to vary continuously in the thickness direction according to a simple power law distribution. Third-order shear deformation theory (HST) of Reddy is modified for FGM plates by considering physical/exact neutral surface. Extended Hamilton’s principle is used to obtain the equations of motion in structural nodes degree of freedom (DOF). Using exact neutral surface in equations of motion, the in-plane and out of plane motions of FGM plates can be separated similar to homogenous plates. The order of equations of motion is reduced using modal reduction method. Shooting method is used to obtain the initial conditions for periodic response. Three bucked equilibrium positions (BEPs) are obtained for FGM plates with immovable boundaries under thermal load. The obtained BEPs are compared with those obtained if the middle surface formulation is used. Also the effects of initial conditions and static pressure on the dynamic response of the system are investigated. It is found that the FGM plate has different responses with the same frequency and amplitude of excitation.