No abstract

No abstract

The generalized cell mapping (GCM) method is used to obtain the stationary response of a single-degree-of-freedom. Vibro-impact system under a colored noise excitation. In order to show the advantage of the GCM method, the stochastic averaging method is also presented. Both of the two methods are tested through concrete examples and verified by the direct numerical simulation. It is shown that the GCM method can well predict the stationary response of this noise-perturbed system no matter whether the noise is wide-band or narrow-band, while the stochastic averaging method is valid only for the wide-band noise.

In this paper, the stochastic stability of a Vibro-impact system with multiple excitation forces is studied. Due to the multiple external excitations, the probability density function (PDF) of the system is extremely difficult to solve. In addition, the existence of coexisting steady states is very common for the Vibro-impact system, and the perturbation of random noise will cause the transitions between the steady states. In this case, we are more interested in working out each attractor's activation energy, which is specifically used to characterize the attractor's stochastic stability, rather than the solution of the PDF.Based on the large deviation theory, the asymptotic analysis is carried out, and a time-varying Hamilton's equation for the quasi-potential 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 (MPEP) for each attractor are derived. Compared with the numerical simulation, it shows very good agreement. Moreover, it is found that the existence of transient chaos near the attractor could seriously deteriorate the attractor's stability.

No abstract