HUANG Dong-mei, XU Wei. Dynamic Responses of Nonlinear Vibro-Impact Systems Under Narrow-Band Random Parametric Excitation[J]. Applied Mathematics and Mechanics, 2016, 37(6): 633-643. doi: 10.3879/j.issn.1000-0887.2016.06.009
Citation: HUANG Dong-mei, XU Wei. Dynamic Responses of Nonlinear Vibro-Impact Systems Under Narrow-Band Random Parametric Excitation[J]. Applied Mathematics and Mechanics, 2016, 37(6): 633-643. doi: 10.3879/j.issn.1000-0887.2016.06.009

Dynamic Responses of Nonlinear Vibro-Impact Systems Under Narrow-Band Random Parametric Excitation

doi: 10.3879/j.issn.1000-0887.2016.06.009
Funds:  The National Natural Science Foundation of China(11472212;11532011)
  • Received Date: 2016-01-04
  • Rev Recd Date: 2016-02-21
  • Publish Date: 2016-06-15
  • The stochastic responses of nonlinear vibro-impact systems under random parametric excitation were investigated. Based on the Krylov-Bogoliubov averaging method, the largest Lyapunov exponent deciding the almost sure stability of the trivial solution was derived. Results show that the characteristics of the largest Lyapunov exponent of the vibro-impact system was different from that of the system without impact. Meanwhile, the backbone curve and the critical equation for the unstable region were also derived in the deterministic case. Then, the 1st- and 2nd-order non-trivial steady-state moments of the system were discussed, and the frequency island phenomenon was also found. Finally, the phenomenon of stochastic jump was analyzed via the finite difference method. The basic jump phenomena indicate that, under the conditions of system parameters within a smaller bandwidth, the most probable motion is around the non-trivial branch of the amplitude response curve, whereas within a larger bandwidth, the most probable motion is around the trivial one of the amplitude response curve.
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