A novel method for evaluation of backbone curve for nonlinear systems identification

PDF(1370 KB)

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (4) : 193-198.

ZHANG Hao1,LI Dongsheng2,LI Hongnan1

Author information +

History +

Abstract

Backbone curves are of great significance for nonlinear identification including detection, characterization, and parameters identification.However, existing methods to extract backbone curves are of complex theories, and there are some problems, such as linearization errors and data fluctuation.A first-order component is main part of harmonic signal, it is convenient to extract backbone curve from instantaneous frequencies of peak points based on the first-order component of free vibration response signal.The proposed method is with simple conception and easy computation, it is suitable to be applied in practice.Three numerical simulations were utilized to verify its effectiveness.Meanwhile, several geometric methods for nonlinear characterization were discussed.Finally, parameter identification of a nonlinear system based on the proposed method was conducted, and good identification results were achieved by comparing with existing method.

Key words

backbone curve / nonlinear identification / nonlinear characterization / parameter identification

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

ZHANG Hao1,LI Dongsheng2,LI Hongnan1. A novel method for evaluation of backbone curve for nonlinear systems identification[J]. Journal of Vibration and Shock, 2020, 39(4): 193-198

References

[1] Kerschen G, Worden K, Vakakis A F, et al. Past, present and future of nonlinear system identification in structural dynamics[J]. Mechanical Systems and Signal Processing, 2006, 20 (3): 505-592.
[2] Worden K, Tomlinson G R. Nonlinearity in Structural Dynamics: Detection, Identification and Modelling[M]. London: Institute of Physics Publishing, 2001. 41-80.
[3] Noël J P, Kerschen G. Nonlinear system identification in structural dynamics: 10 more years of progress[J]. Mechanical Systems and Signal Processing, 2017, 83: 2-35.
[4] Rosenberg R M. The normal modes of nonlinear n-degree-of-freedom systems[J]. Journal of Applied Mechanics, 1962, 29(1): 7-14.
[5] Shaw S W, Pierre C. Non-linear normal modes and invariant manifolds [J]. Journal of Sound and Vibration, 1991, 150(1): 170–173.
[6] 吴志强, 陈予恕, 毕勤胜. 非线性模态的分类和新的求解方法[J]. 力学学报, 1996, 28(3): 298-307.
Wu Zhiqiang, Chen Yushu, Bi Qinsheng. Classification of nonlinear normal modes and their new constructive method[J]. Acta Mechanica Sinica, 1996, 28(3): 298-307.
[7] Kerschen G, Peeters M, Golinval J C, et al. Nonlinear normal modes, Part I: A useful framework for the structural dynamicis[J]. Mechanical Systems and Signal Processing, 2009, 23(1): 170-194.
[8] Londoño J M, Cooper J E, Neild S A. Identification of systems containing nonlinear stiffnesses using backbone curves[J]. Mechanical Systems and Signal Processing, 2017, 84: 116-135.
[9] Londoño J M, Neild S A, Cooper J E. Identification of backbone curves of nonlinear systems from resonance decay responses[J]. Journal of Sound and Vibration, 2015, 348: 224-238.
[10] Feldman M. Non-linear system vibration analysis using Hilbert Transform I: Free vibration analysis method Freevib[J]. Mechanical Systems and Signal Processing, 1994, 8(2): 119-127.
[11] 王立岩, 李东升, 李宏男. 基于HHT的非线性振动系统参数识别研究[J]. 工程力学, 2017, 34(1): 40-44+56.
Wang Liyan, Li Dongsheng, Li Hongnan. Parameter identification of nonlinear vibration systems based on the Hilbert-Huang transform[J]. Engineering Mechanics, 2017, 34(1): 40-44+56.
[12] Carrella A, Ewins D J. Identifying and quantifying structural nonlinearities in engineering applications from measured frequency response functions[J]. Mechanical Systems and Signal Processing, 2011, 25(3): 1011-1027.
[13] 李庆扬, 王能超, 易大义. 第5版. 数值分析[M]. 北京: 清华大学出版社, 2008. 39-40.
Li Qingyang, Wang Nengchao, Yi Dayi. 5th edition. Numerical Analysis[M]. Beijing: Tsinghua University Press, 2008:39-40.
[14] Renson L, Gonzalez-Buelga A, Barton D A W, et al. Robust identification of backbone curves using control-based continuation[J]. Journal of Sound and Vibration, 2016, 367: 145-158.
[15] Peter S, Riethmüller R, Leine R I. Tracking of backbone curves of nonlinear systems using Phase-Locked-Loops [C]//Kerschen G. Nonlinear Dynamics, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series. New York: Springer, 2016. 107-120.
[16] 王兴. 局部非线性结构的动力学计算与试验辨识研究[D]. 北京: 清华大学, 2016. 42-43.
Wang Xing. Calculation and identification of structures with localized nonlinearities[D]. Beijing: Tsinghua University, 2016. 107-120.
[17] Wang Z C, Ren W X, Chen G D. Time-varying linear and nonlinear structural identification with analytical mode decomposition and hilbert transform[J]. Journal of Structural Engineering-ASCE, 2013, 139: 06013001.
[18] 王佐才, 任伟新, 邢云斐. 基于解析模态分解的时变与弱非线性结构密集模态参数识别[J]. 振动与冲击, 2014, 33(19): 1-7+16.
Wang Zuocai, Ren Weixin, Xing Yunfei. Analytical modal decomposition-based time-varying and weakly nonlinear structures' modal parametric identification with closely-spaced modes[J]. Journal of Shock and Vibration, 2014, 33(19): 1-7+16.
[19] Kovacic I, Brennan M J. The Duffing Equation: Nonlinear Oscillators and their Behaviour[M]. New Jersey: John Wiley & Sons, 2011. 25-53.
[20] Londoño J M, Cooper J E, Neild S A. Identification of systems containing nonlinear stiffnesses using backbone curves[J]. Mechanical Systems and Signal Processing, 2017, 84: 116-135.
[21] 萧寒. 多自由度非线性系统的霍普分岔与鞍结分岔控制[D]. 长沙: 湖南大学, 2008, 29-30.
Xiao Han. Hopf and saddle-node bifurcation control in multiple-degree-of-freedom nonlinear systems[D]. Changsha: Hunan University, 2008, 29-30.
[22] Al-Hadid M A, Wright J R. Developments in the force-state mapping technique for non-linear systems and the extension to the location of non-linear elements in a lumped-parameter system[J]. Mechanical Systems and Signal Processing, 1989, 3(3):269-290.