Nonlinear dynamic thermoelastic response of rectangular FGM plates with longitudinal velocity

This study investigates nonlinear dynamic thermoelastic response of functionally graded material (FGM) plates with longitudinal velocity for the first time. The large amplitude motion of FGM plates is considered so that the present model includes both geometry and material nonlinearities. Based on the D'Alembert's principle, the out-of-plane equation of motion of the system is obtained by considering the thermal effect and the longitudinal velocity. After that, the Galerkin method is employed to discretize the partial differential equation of motion to a set of ordinary differential equations. The method of harmonic balance is used to solve analytically the time-varying set of ordinary differential equations. The approximately analytical solutions are verified by numerical solutions utilizing an adaptive step-size fourth-order Runge-Kutta technique. Furthermore, the stability of steady-state response is analyzed for the approximately analytical solutions. The linear frequency characteristics and nonlinear frequency-response characteristics are both presented for the system. The nonlinear frequency-response relationships demonstrate strong hardening-type behavior of the system. Results are shown to examine the influences of different parameters including longitudinal velocity, temperature, constituent volume distribution, in-plane pretension, damping and force amplitude on the nonlinear dynamic thermoelastic response of FGM plates with longitudinal velocity.