Chaos of vibro-impact system under harmonic and white noise excitations.

Discontinuity generally induces the characteristic of strong nonlinear and singularity for vibro-impact systems. Chaos in a vibro-impact system under harmonic and white noise excitations is investigated. Based on dynamical theory and Melnikov method, the homoclinic orbits are studied and the critical value of onset of Smale chaos is given analytically. Additively, this analytical results are verified by numerical simulations, including Phase diagram, Poincare section and safe basins. The results reveals that the conclusion via Melnikov method is the necessary condition for onset of chaos motion, and the necessary and sufficient condition for the erosion of safe basin. [ABSTRACT FROM AUTHOR]