Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier

Wei Xu, Dong Mei Huang, Wen Xian Xie

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2 引用 (Scopus)

摘要

In this paper, multi-valued responses and dynamic properties of a nonlinear vibro-impact system with a unilateral nonzero offset barrier are studied. Based on the Krylov-Bogoliubov averaging method and Zhuravlev non-smooth transformation, the frequency response, stability conditions, and the equation of backbone curve are derived. Results show that in some conditions impact system may have two or four steady-state solutions, which are interesting and not mentioned for a vibro-impact system with the existence of frequency island phenomena. Then, the classification of the steady-state solutions is discussed, and it is shown that the nontrivial steady-state solutions may lose stability by saddle node bifurcation and Hopf bifurcation. Furthermore, a criterion for avoiding the jump phenomenon is derived and verified. Lastly, it is found that the distance between the system's static equilibrium position and the barrier can lead to jump phenomenon under hardening type of nonlinearity stiffness.

源语言英语
文章编号030502
期刊Chinese Physics B
25
3
DOI
出版状态已出版 - 20 1月 2016

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