The determination of the activation energy for a vibro-impact system under multiple excitations

In this paper, the stochastic stability of a vibro-impact system with multiple excitation forces is studied. Due to the multiple external excitations and the coexistence of metastable states, the solution of each attractor's activation energy, which is specifically used to characterize the attractor's stochastic stability, is much more suitable for the stability analysis rather than the solution of the probability density function. Based on the large deviation theory, the asymptotic analysis is carried out, and a time-varying Hamilton's equation for the quasi-potential of the vibro-impact system is derived. To verify the effectiveness of the theoretical analysis, two detailed examples, where an impact attractor and a non-impactor coexist in the system, are conducted. By the application of the action plot method, the activation energies and the most probable exit paths for each attractor are derived. Compared with the numerical simulation, the results show very good agreement. Moreover, it shows that the existence of transient chaos near the attractor could seriously deteriorate the attractor's stability.