Two Degrees Of Freedom Nonlinear System Of Non-white Noise Excitation And Collision Vibration System's Response

The stationary response of single-degree-of-freedom (SDOF) vibro-impact system under wide-band random excitation is studied. The approximate stationary responses of the system are obtained by using the stochastic averaging method for strongly non-linear SDOF system under wide-band random excitation. Two examples with both side constraints and with right hand side constraint only are given to illustrate the application and accuracy of the proposed procedure. It is shown that the analytical stationary probability densities of the system agree well with those from digital simulation of the original equation of motion. Then a stochastic averaging procedure for coupled Duffing-van der Pol oscillators subject to wide-band random excitations or to combined harmonic and white noise excitations is proposed and the averaged Fokker-Plank-Kolmogorov(FPK) equation is solved by using the finite difference method. It shown that the analytical results are in very good agreement with those from digital simulation of the original equation of motion. The stochastic jump of the coupled Duffing-van der Pol oscillators under combined harmonic and white noise excitations and its bifurcation as the system parameters change are examined. The differences between the deterministic bifurcation and stochastic bifurcation are pointed out and the reasonable explanation of the phenomena to given.