Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

doi:10.1088/1674-1056/24/4/040502

中国物理B ›› 2015, Vol. 24 ›› Issue (4): 40502-040502.doi: 10.1088/1674-1056/24/4/040502

Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

黄冬梅^{a b}, 徐伟^a, 谢文贤^{a b}, 韩群^a

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

收稿日期:2014-09-11 修回日期:2014-10-23 出版日期:2015-04-05 发布日期:2015-04-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11302170, and 11302172).

Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

Huang Dong-Mei (黄冬梅)^{a b}, Xu Wei (徐伟)^a, Xie Wen-Xian (谢文贤)^{a b}, Han Qun (韩群)^a

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

Received:2014-09-11 Revised:2014-10-23 Online:2015-04-05 Published:2015-04-05
Contact: Xu Wei E-mail:weixu@nwpu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11172233, 11302170, and 11302172).

摘要/Abstract

摘要：

In this paper, the principal resonance response of a stochastically driven elastic impact (EI) system with time-delayed cubic velocity feedback is investigated. Firstly, based on the method of multiple scales, the steady-state response and its dynamic stability are analyzed in deterministic and stochastic cases, respectively. It is shown that for the case of the multi-valued response with the frequency island phenomenon, only the smallest amplitude of the steady-state response is stable under a certain time delay, which is different from the case of the traditional frequency response. Then, a design criterion is proposed to suppress the jump phenomenon, which is induced by the saddle-node bifurcation. The effects of the feedback parameters on the steady-state responses, as well as the size, shape, and location of stability regions are studied. Results show that the system responses and the stability boundaries are highly dependent on these parameters. Furthermore, with the purpose of suppressing the amplitude peak and governing the resonance stability, appropriate feedback gain and time delay are derived.

关键词: elastic impact system, time delay, frequency island, jump avoidance

Abstract:

Key words: elastic impact system, time delay, frequency island, jump avoidance

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

02.60.Cb (Numerical simulation; solution of equations)

黄冬梅, 徐伟, 谢文贤, 韩群. Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback[J]. 中国物理B, 2015, 24(4): 40502-040502.

Huang Dong-Mei (黄冬梅), Xu Wei (徐伟), Xie Wen-Xian (谢文贤), Han Qun (韩群). Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback[J]. Chin. Phys. B, 2015, 24(4): 40502-040502.

参考文献 33

[1]	Tomlinson G R and Lam J 1984 J. Sound Vib. 96 111
[2]	Lin W, Ni Q and Huang Y 2006 J. Sound Vib. 296 1068
[3]	Souza S L T, Wiercigroch M, Caldasb I L and Balthazarc J M 2008 Chaos, Solitons and Fractals 38 864
[4]	Wang L, Yue X L, Sun C Y and Xu W 2013 Nonlinear Dyn. 71 597
[5]	Yin S, Ding S X, Xie X C and Luo H 2014 IEEE Trans. Ind. Electron. 61 6418
[6]	Yin S, Zhu X P, and Kaynak O 2014 IEEE Trans. Ind. Electron.
[7]	Hu H Y, Dowell E H and Virgin L N 1998 Nonlinear Dyn. 15 311
[8]	Hu H Y, Wang Z H 2002 Dynamics of Controlled Mechanical Systems with Delayed Feedback (Berlin/Heidelberg: Springer-Verlag)
[9]	Maccari A 2001 Nonlinear Dyn. 26 105
[10]	Xu J and Yu P 2004 Int. J. Bifurc. Chaos 14 2777
[11]	Nayfeh N A and Baumann W T 2008 Nonlinear Dyn. 53 75
[12]	Paola M D and Pirrotta A 2011 Probab. Eng. Mech. 16 43
[13]	Jin Y F and Hu H Y 2007 Nonlinear Dyn. 50 213
[14]	Zhang H Q, Xu W, Xu Y and Li D X 2009 Physica A 388 3017
[15]	Ren H P, Li W C, and Liu D 2010 Chin. Phys. B 19 030511
[16]	Tian J and Chen Y 2010 Chin. Phys. Lett. 27 030502
[17]	Yang X L and Sun Z K 2010 Int. J. Non-Linear Mech. 45 621
[18]	Wang J A 2011 Chin. Phys. B 20 120701
[19]	Gu W D, Sun Z Y, Wu X M and Yu C B 2013 Chin. Phys. B 22 080507
[20]	Yin S, Wang G and Yang X 2014 Int. J. Syst. Sci. 45 1375
[21]	Saha A and Wahi P 2014 Int. J. Non-Linear Mech. 63 60
[22]	Gao X and Chen Q 2014 J. Sound Vib. 333 1562
[23]	Yin S, Wang G and Karimi H R 2014 Mechatronics 24 298
[24]	Yin S, Ding S X, Haghani A, Hao H and Zhang P 2012 J. Process. Control 22 1567
[25]	Liu Y, Waters T P and Brennan M J 2005 J. Sound Vib. 280 21
[26]	Weding W V 1990 Struct. Saf. 8 13
[27]	Schmidt G and Tondl A 1986 Nonlinear Vibrations (Cambridge: Cambridge University Press)
[28]	Deshpande S, Mehta S and Jazarv G N 2006 Int. J. Mech. Sci. 48 341
[29]	Jazar G N, Houim R, Narimani A and Golnaraghi M F 2006 J. Vib. Control 12 1205
[30]	Shinozuka M 1972 J. Sound Vib. 25 111
[31]	Zhu W Q 1998 Random Vibration (Beijing: Science Press)
[32]	Rong H W, Wang X D, Xu W and Fang T 2008 Acta Phy. Sin. 57 6888 (in Chinese)
[33]	Daqaq M F and Vogl G W 2008 Proc. 6th EUROMECH Nonlinear Dynamics Conf., Saint Petersburg, Russia

Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

Principal resonance response of a stochastic elastic impact oscillator under nonlinear delayed state feedback

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays[J]. 中国物理B, 2023, 32(3): 38701-038701.
[2]	Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Effect of autaptic delay signal on spike-timing precision of single neuron[J]. 中国物理B, 2023, 32(3): 38703-038703.
[3]	Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Inferring interactions of time-delayed dynamic networks by random state variable resetting[J]. 中国物理B, 2022, 31(3): 30502-030502.
[4]	Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics[J]. 中国物理B, 2022, 31(3): 33101-033101.
[5]	Wenjie Yang(杨文杰). Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation[J]. 中国物理B, 2022, 31(2): 20201-020201.
[6]	Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay[J]. 中国物理B, 2022, 31(10): 100201-100201.
[7]	Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶). Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns[J]. 中国物理B, 2021, 30(5): 50502-050502.
[8]	Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Stabilization strategy of a car-following model with multiple time delays of the drivers[J]. 中国物理B, 2021, 30(12): 120506-120506.
[9]	Guoyuan Qi(齐国元) and Zimou Wang(王子谋). Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay[J]. 中国物理B, 2021, 30(12): 120516-120516.
[10]	黄玉娇, 袁孝焰, 杨旭华, 龙海霞, 肖杰. Multiple Lagrange stability and Lyapunov asymptotical stability of delayed fractional-order Cohen-Grossberg neural networks[J]. 中国物理B, 2020, 29(2): 20703-020703.
[11]	魏长立, 赵曦. Validity of extracting photoionization time delay from the first moment of streaking spectrogram[J]. 中国物理B, 2019, 28(1): 13201-013201.
[12]	钱郁, 高红艳, 姚成贵, 崔晓华, 马军. Synchronization performance in time-delayed random networks induced by diversity in system parameter[J]. 中国物理B, 2018, 27(10): 108902-108902.
[13]	杨增强, 叶地发, 傅立斌. Attosecond transient absorption spectroscopy: Comparative study based on three-level modeling[J]. 中国物理B, 2018, 27(1): 13301-013301.
[14]	王莉芳, 仇康, 贾亚. Effects of time delays in a mathematical bone model[J]. 中国物理B, 2017, 26(3): 30503-030503.
[15]	王雪峰, 王元庆, 苏金善, 杨兴雨. Locating the position of objects in non-line-of-sight based on time delay estimation[J]. 中国物理B, 2016, 25(8): 84203-084203.