&nbsp;The complex dynamics of a relative rotation system and its control by delay velocity feedback

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Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (12) : 127-132.

The complex dynamics of a relative rotation system and its control by delay velocity feedback

SHANG Hui-lin LI Wei-yang HAN Yuan-bo

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Abstract

The complex dynamics in a typical relative rotation system such as chaos and erosion of safe basin induced by the variation of system parameters was investigated in this paper. In order to keep the reliability of the oscillation of the system, delayed velocity feedback was applied in the system to suppress these complex dynamical behaviors. The critical excitation for chaos and erosion of safe basin of the delayed velocity feedback controlled system was obtained by the Melnikov method. Then complex dynamical behaviors of the systems under different system parameters were stimulated numerically which verified the validity of the theoretical prediction. It was found that the delayed velocity feedback could be used as an effective method on suppressing chaos and erosion of safe basin of the relative rotation system.

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SHANG Hui-lin LI Wei-yang HAN Yuan-bo. The complex dynamics of a relative rotation system and its control by delay velocity feedback[J]. Journal of Vibration and Shock, 2015, 34(12): 127-132

References

[1] 赵武，刘彬，石培明，等.一类非线性相对转动周期系统的平衡稳定性分析[J]. 物理学报, 2006, 55(8): 3852-3857.
Zhao Wu, Liu Bin, Shi Pei-ming, et al. Anslysis of stability of the equilibrium state of periodic motion in a nonlinear relative rotation system [J]. Acta Physica Sinica, 2006, 55(8): 3852-3857.
[2] 刘爽，刘彬，张业宽，等.一类时滞非线性相对转动系统的Hopf分岔与周期解的稳定性[J].物理学报，2010, 59(1): 38-43.
LIU Shuang, LIU Bin, ZHANG Ye-kuan, et al. Hopf bifurcation and stability of periodic solutions in a nonlinear relative rotation dynamical system with time delay [J]. Acta Physica Sinica, 2010, 59(1): 38-43.
[3] 刘浩然，朱占龙，石培明.一类相对转动的时滞非线性动力系统的稳定性分析[J]. 物理学报，2010, 59(10): 6770-6771.
LIU Hao-ran, ZHU Zhan-long, SHI Pei-ming. Stability analysis of a relative rotation time-delay nonlinear dynamic system [J]. Acta Physica Sinica, 2010, 59(10): 6770-6771.
[4] 张文明，李雪，刘爽，等.一类非线性相对转动系统的混沌运动及多时滞反馈控制[J].物理学报, 2013, 62(9): 095402.
ZHANG Wen-ming, LI Xue, LIU Shuang, et al. Chaos and the control of multi-time delay feedback for some nonlinear relative rotation system [J]. Acta Physica Sinica, 2013, 62(9): 095402.
[5] 乔杰敏，王坤，李秀菊，等.两类相对转动非线性动力学系统的统一动力学模型及混沌运动[J]. 燕山大学报, 2009, 33(2): 159-162.
QIAO Jie-min, WANG Kun, LI Xiu-ju, et al. Unified dynamics model of two kind of relative rotation nonlinear dynamics system and chaos[J]. Journal of Yanshan University, 2009, 33(2): 159-162.
[6] 候东晓，赵红旭，刘彬.一类含Mathieu-Duffing振子的相对转动系统的分岔和混沌[J]. 物理学报，2013, 62(23) : 234501.
HOU Dong-xiao, ZHAO Hong-xu, LIU Bin. Bifurcation and chaos in some relative rotation systems with Mathieu-Duffing oscillator [J]. Acta Physica Sinica, 2013, 62(23): 234501.
[7] Luo S K. The theory of relativistic analytical mechanics of the rotational systems. Applied Mathematics and Mechanics (English Edition), 1998, 19(1): 45-57.
[8] Thompson J M T, Rainey F C T, Soliman M S. Ship stability criteria based on chaotic transients from incursive fractals[J]. Philosophical Transactions of the Royal Society, 1995, 332(1): 149-167.
[9] Gan C B. Noise-Induced chaos and basin erosion in softening Duffing oscillator [J]. Chaos, Solitons and Fractals, 2005, 25(5): 1069-1081.
[10] Rega G, Valeria S. Bifurcation, response scenarios and dynamic integrity in a single-mode model of noncontact atomic force microscopy [J]. Nonlinear Dynamics, 2013, 73(1-2): 101-123.
[11] Xu J, Yu P. Delay-induced bifurcations in a nonautonomous system with delayed velocity feedbacks [J]. International Journal of Bifurcation and Chaos, 2004, 14(8): 2777-2798.
[12] Shao S, Masti K M, Younis M I. The effect of time-delayed feedback controller on an electrically actuated resonator [J]. Nonlinear Dynamics, 2013, 74(1-2): 257-270.
[13] Alsaleem F M, Younis M I. Stabilization of electrostatic MEMS resonators using a delayed feedback controller [J]. Smart Materials and Structures, 2010, 19(3): 035016.
[14] 尚慧琳,文永蓬.软弹簧Duffing系统的安全域侵蚀及其时滞速度反馈控制[J].振动与冲击,2012, 31(8): 11-15.
SHANG Hui-lin，WEN Yong-peng Erosion of safe basins in a softening duffing system and its control with time-delay position feedback[J]. Journal of vibration and shock, 2012, 31(8):11-15.
[15] Shang H L. Control of Fractal Erosion of Safe Basins in a Holmes-Duffing System via Delayed Position Feedbacks [J]. Chinese Physics Letters, 2011, 28(1): 010502.
[16] Shang H L, Xu J. Delayed feedbacks to control the fractal erosion of safe basins in a parametrically excited system [J]. Chaos, Solitons and Fractals, 2009, 41(4): 1880-1896.
[17] Thomsen J J, Fidlin A. Analytical approximations for stick-slip vibration amplitudes [J]. International Journal of Nonlinear Mechanics, 2003, 38(3): 389-403