Dynamical analysis of vibro-impact capsule system with Hertzian contact model and random perturbation excitations

In this paper, the modeling and dynamical response of a vibro-impact capsule system with Hertzian contact and random environmental perturbation is studied. The capsule system is modeled as a two-degree-of-freedom dynamical system composed of a rigid capsule and a movable internal mass. The random environmental perturbation is incorporated in the models of the capsule system, which is more realistic working condition of capsule robotic system. The impact between the rigid capsule and the internal mass will occur when the relative displacement is larger than the gap between them. The impact interaction is described by using the Hertzian contact model. The resistance force between the capsule and the sliding face is described by Coulomb friction model. The response of the vibro-impact capsule system is obtained through Monte Carlo simulation. A kind of random stick-slip phenomena can be found in the response of the proposed model, which is consistent with the actual behavior of capsule system. At last, it is worthy noting that stochastic P-bifurcation occurs when the parameters of the system vary.