Periodicity in the response of nonlinear plate, under moving mass

The dynamics of nonlinear thin plates under influence of relatively heavy moving masses is considered. By expansion of the solution as a series of mode functions, the governing equations of motion are reduced to an ordinary differential equation for time development of vibration amplitude, which is Duffingʹs oscillator with time varying coefficients. Through the application of Banachʹs fixed-point theorem, the periodic solutions are predicted. The method presented in this paper is general so that the response of plate to moving force systems can also be considered.