Stationary response analysis of vibro-impact system with a unilateral nonzero offset barrier and viscoelastic damping under random excitations

The stationary response analysis of stochastic vibro-impact (VI) dynamical system with a unilateral nonzero offset barrier and viscoelastic damping under additive and multiplicative random excitations is explored. First, the conversion of the original stochastic VI system coupled with viscoelastic damping into an equivalent stochastic VI system without viscoelastic damping terms is performed by adding the equivalent stiffness and damping. Then, the equivalent stochastic VI system is studied according to the level of system energy instead of non-smooth transformation of the previous literature; thus, description on effects of impacts draws support from the loss of the system energy. The energy loss at each impact is found to be related to the restitution factor and the energy level before impact. Furthermore, the probability density functions of the equivalent VI system based on assumption of the weak damping and random perturbation is produced by the application of the stochastic averaging of energy envelope. The effectiveness of the suggested method is verified by comparing the analytical results with those from Monte Carlo simulations.