Steady-state Response Of Bilateral Asymmetric Vibro-impact System To Stochastic Excitation

The vibro-impact system is an important kind of nonlinear system. In this paper, the stationary response of vibro-impact system under white noise process is gained through both theoretical analysis and Monte-Carlo simulation. Many interesting dynamical phenomena are found in such kind of systems. The main works and conclusions are listed as follows:Firstly, the responses of the Duffing oscillator with single-sided barrier and bilateral asymmetric barrier vibro-impact system to combined harmonic and random excitation are investigated. Some special phenomena are found in these systems, like grazing bifurcation, period-adding bifurcation. It is also found that the response of system to random excitation is different from smooth system, and in some critical situations, the noise can even change the dynamics property of the system.Secondly, the stochastic averaging method is used to study a SDOF vibro-impact system, and FPK equation and the steady-state response of the system are obtained.Finally, the stationary probability densities of amplitude, total energy and the joint probability density of displacement and velocity of the system are presented in the end of this paper. All these results agreed well with these from Monte-Carlo simulation of the original equation of motion.