Chaotic vibration study based on two-well potential theory

PDF(3089 KB)

Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (24) : 23-29.

LIU Shuyong WEI Xiulei WANG Ji YU Xiang

Author information +

History +

Abstract

The multiscale method was applied to solve the approximate analytical solution to a two-well potential system’s free vibration response. The effects of fast varying components and slow varying ones in the system response on the response were analyzed. The amplitude-frequency relationship of the system was obtained with the averaging method. The tongue shape structural curve of the vibration amplitude versus the frequency regulation factor was gained, it revealed the system’s nonlinear essential characteristics. To verify the theoretical results, a test rig of magnetic absorbing leaf spring based on the two-well potential theory was designed here. The response characteristics of this system subjected to different excitation amplitudes and frequencies were studied. Subharmonic phenomena, superharmonic phenomena and different modes of period-1 motion of the system were observed. Meanwhile, through changing parameters of the system, continuous and stable chaotic vibration was excited under the condition of a certain frequency and excitation amplitude. The strange attractors of the measured signals were reconstructed with the phase space reconstruction technique. The maximum Lyapunov exponent and correlation dimension number of chaotic signals were calculated. Results were beneficial to the application of chaos phenomena in engineering.

Key words

two-well potential / chaotic vibration / multiscale method / nonlinear time series

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LIU Shuyong WEI Xiulei WANG Ji YU Xiang. Chaotic vibration study based on two-well potential theory[J]. Journal of Vibration and Shock, 2017, 36(24): 23-29

References

[1] Samuel Zambrano，Juan Sabuco. How to minimize the control frequency to sustain transient chaos using partial control[J]. Communications in Nonlinear Science and Numerical Simulation，2014，19(3)：726-737.
[2] Xiang Yu，Shijian Zhu，Shuyong Liu. A new method for line spectra reduction similar to generalized synchronization of chaos[J]. Journal of Sound and Vibration，2007，306（3-5）：835-848.
[3] 俞翔,朱石坚,楼京俊. 基于碰撞振动的隔振系统混沌化实验研究，[J].振动与冲击,2014,33(18):59-64
Yuxiang, Zhu shijian, Lou jingjun. Tests for chaotification method of a vibration isolation system with a vibro-impact subsystem [J].Journal of Vibration and Shock,2014,33(18):59-64.
[4] 龙运佳，杨勇，王聪玲. 基于混沌振动力学的压路机工程[J]. 中国工程科学，2000，2（9）：76-79.
Long Yunjia，Yang Yong，Wang Congling. Road roller engineering based on chaotic vibration mechanics[J]. Engineering Science，2000，2（9）：76-79.
[5] 韩建群，郑萍.一种简单的Lorenz混沌振动主动隔振方法[J].系统工程与电子技术，2006，128(10)：1566-1568.
Han Jianqun，Zheng Ping. Active control isolation for the Lorenz chaotic vibration with a simple method[J]. Systems Engineering and Electronics，2006，128(10)：1566-1568.
[6] 高远，耿兆云，范健文. 汽车悬架系统中混沌振动的自适应跟踪控制研究[J]. 机械设计与制造. 2013，12 ：198-201.
Gao Yuan，Geng Zhaoyun，Fan Jianwen. Control chaos in automobile suspension system via adaptive tracking control method[J]. Machinery Design & Manufacture，2013，12 ：198-201.
[7] 熊怀,孔宪仁,刘源.阻尼对耦合非线性能量阱系统影响研究[J].振动与冲击,2015,34(11):116-121.
XIONG Huai, KONG Xian-ren, LIU Yuan. Influence of structural damping on a system with nonlinear energy sinks[J].Journal of Vibration and Shock,2015,34(11):116-121.
[8] MARIAN WIERCIGROCH，VICTOR W. T. SIN. Measurement of Chaotic Vibration in a Symmetrically Piecewise Linear Oscillator[J]. Chaos，Solitons & Fractals，1998，19(1-2)：209-220.
[9] 陈立群，刘延柱.混沌振动系统的开闭环控制[J].应用科学学报，1999，17(4)：445-449.
Chen Liqun，Liu Yanzhu. The open-plus-closed-loop control for chaotic oscillations[J]. JOURNAL OF APPLIED SCIENCES，1999，17(4)：445-449.
[10] 韩保红，马英忱，闫石. 用Matlab仿真非线性混沌振动的主动隔振研究[J]. 控制与决策，2003，18(1)：120-122.
Han Baohong，Ma Yingchen，Yan Shi. Active control isolation research for a class of nonlinear chaotic vibration systems[J]. Control and Decision，2003，18(1)：120-122.
[11] 韩保红，闫石，焦耀斌，马英忱.一类非线性混沌振动的主动隔振实验研究[J]. 噪声与振动控制，2002，2：24-28.
Han Baohong，Yan Shi，Jiao Yaobin，Ma Yingchen. Active control isolation research for a class of nonlinear chaotic vibration systems[J]. Noise and Vibration Control，2002，2：24-28.
[12] 梁山，郑剑，朱勤，刘飞. 非线性车辆模型混沌振动的仿真与实验研究[J]. 机械强度，2012，34(1)：6-12.
Liang Shan，Zheng Jian，Zhu Qin，Liu Fei. Numerical and experimental investigations on chaotic vibration of a nonlinear vehicle model over road excitation[J]. Journal of Mechanical Strength，2012，34(1)：6-12.
[13] Katsutoshi Yoshida，Keijin Sato Yamamoto，Kazutaka Yokota. Characterization of chaotic vibration without system equations[J]. Int. J. Non-linear Mechanics，1997，32(3)：547-562.
[14] 任成龙，葛翔. 悬架混沌振动台的设计[J].南京工程学院学报（自然科学版），2009，7（4）：37-42.
Ren Chenglong，Ge Xiang. Design of suspension chaotic vibration table[J]. Journal of Nanjing Institute of Technology（Natural Science Edition），2009，7（4）：37-42.
[15] Francis C. Moon. Chaotic Vibrations An Introduction for Applied Scientists and Engineers[M]. New York，1987.
[16] Yan Yan, Wenquan Wang, Lixiang Zhang. Applied multiscale method to analysis of nonlinear vibration for double-walled carbon nanotubes. Applied Mathematical Modelling ,2011. 35: 2279–2289.
[17] Lewis Mitchell and Georg A. Gottwald.On finite-size Lyapunov exponents in multiscale systems. Chaos,2012.22: 1-9.
[18] T. Okabe, T.Kondou, J.Ohnishi.Elliptic averaging methods using the sum of Jacobian elliptic delta and zeta functions as the generating solution International Journal of Non-Linear Mechanics. 2011,46: 159–169.