Asymptotic analysis of nonlinear vibration of an elastic plate under heavy fluid loading

The objective of this paper is identification and analysis of excitation regimes, when nonlinear effects are pronouncedly developed in the stationary dynamics of an infinitely long uniform elastic plate under heavy fluid loading. The method of multiple scales is applied and the solutions of the amplitude modulation equations for two types of excitation are obtained in a closed analytical form. Results of the asymptotic analysis reported in this paper highlight several aspects of the nonlinear dynamics of such a plate, which have not previously been studied in detail. It is shown that for 'weak' excitation of a resonant wave the stationary response is controlled by the structure-originated nonlinearity, whereas for 'strong' sub-harmonic excitation the stationary response is controlled by the fluid-originated nonlinearity. In both these cases, a dependence of the amplitudes of directly and indirectly excited resonant waves on the amplitude of the driving force is determined.