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

doi:10.1088/1674-1056/25/3/030502

中国物理B ›› 2016, Vol. 25 ›› Issue (3): 30502-030502.doi: 10.1088/1674-1056/25/3/030502

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

Wei Xu(徐伟), Dong-Mei Huang(黄冬梅), Wen-Xian Xie(谢文贤)

1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Department of Civil and Environmental Engineering, Rice University, Houston 77005, USA

收稿日期:2015-08-05 修回日期:2015-09-29 出版日期:2016-03-05 发布日期:2016-03-05
通讯作者: Dong-Mei Huang E-mail:dongmeihuang1@hotmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11472212, 11532011, 11302171, and 11302172).

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

Wei Xu(徐伟)¹, Dong-Mei Huang(黄冬梅)^1,2, Wen-Xian Xie(谢文贤)¹

1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2. Department of Civil and Environmental Engineering, Rice University, Houston 77005, USA

Received:2015-08-05 Revised:2015-09-29 Online:2016-03-05 Published:2016-03-05
Contact: Dong-Mei Huang E-mail:dongmeihuang1@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11472212, 11532011, 11302171, and 11302172).

摘要/Abstract

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.

关键词: vibro-impact system, multi-valued response, frequency island, stability

Abstract: 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.

Key words: vibro-impact system, multi-valued response, frequency island, stability

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

02.60.Cb (Numerical simulation; solution of equations)

徐伟, 黄冬梅, 谢文贤. Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier[J]. 中国物理B, 2016, 25(3): 30502-030502.

Wei Xu(徐伟), Dong-Mei Huang(黄冬梅), Wen-Xian Xie(谢文贤). Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier[J]. Chin. Phys. B, 2016, 25(3): 30502-030502.

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

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

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