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一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

时培明 李纪召 刘彬 韩东颖

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一类准周期参激非线性相对转动动力系统的稳定性与时滞反馈控制

时培明, 李纪召, 刘彬, 韩东颖

Stability and time-delayed feedback control of a relative-rotation nonlinear dynamical system under quasic-periodic parametric excitation

Li Ji-Zhao, Liu Bin, Han Dong-Ying, Shi Pei-Ming
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  • 建立了一类含准周期参数激励和时滞反馈的相对转动非线性系统的动力学方程. 采用多尺度法求解1/2亚谐波主参数共振下的分岔响应方程,并分析了系统的稳定性. 在求解非受控系统的定常解的基础上,通过讨论系统的动力学特性,研究了准周期参数激励对系统响应的影响. 采用时滞反馈控制的方法对系统分岔和极限环(域)进行控制,数值模拟的结果表明通过改变时滞参数可以实现对系统分岔的控制,并能有效地控制极限环(域)的幅值和稳定性.
    The dynamical equation of a relative-rotation nonlinear dynamic system, which contains quasi-periodic parametric excitation and time delays, is established. Bifurcation response equation of 1/2 subharmonic primary parametric resonance is obtained by the method of multiple scales, and the stability of the system is analyzed. By solving the steady state solutions of the uncontrolled system, the effect of quasi-periodic parametric excitation on system response is studied through discussing the dynamics of the system. Time-delay feedback control method is used to control the bifurcation and limit cycle(region). Numerical results show that the bifurcation and the stability of the limit cycle(region) are controlled effectively by changing the time-delay parameters.
    • 基金项目: 国家自然科学基金(批准号: 51005196)和河北省自然科学基金(批准号: F2010001317)资助的课题.
    [1]

    Carmeli M 1985 Found. Phys. 15 175

    [2]

    Carmeli M 1986 Inter. J. Theor. Phys. 15 89

    [3]

    Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]

    [4]

    Luo S K 1998 Appl. Math. Mech. 19 45

    [5]

    Fu J L, Chen X W, Luo S K 1999 Appl. Math. Mech. 20 1266

    [6]

    Fu J L, Chen X W, Luo S K 2000 Appl. Math. Mech. 21 549

    [7]

    Luo S K, Guo Y X, Chen X W 2001 Acta Phys. Sin. 50 2053 (in Chinese) [罗绍凯、 郭永新、 陈向炜 2001 物理学报 50 2053]

    [8]

    Luo S K 2002 Chin. Phys. Lett . 19 449

    [9]

    Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523

    [10]

    Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004物理学报 53 5]

    [11]

    Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271

    [12]

    Fang J H 2000 Acta Phys. Sin. 49 1028 (in Chinese) [方建会 2000 物理学报 49 1028]

    [13]

    Jia L Q 2003 Acta Phys. Sin. 52 1039 (in Chinese) [贾利群 2003 物理学报 52 1039]

    [14]

    Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林、 刘 彬 2002 物理学报 51 2191]

    [15]

    Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明、 刘 彬、 侯东晓 2008 物理学报 57 1321]

    [16]

    Shi P M, Liu B,Hou D X 2009 Chinese Journal of Mechanical Engineering 22 132

    [17]

    Belhaq M, Guennoun K, Houssni M 2002 Int. J. Non-Lin Mech. 37 445

    [18]

    Guennoun K, Belhaq M, Houssni M 2002 Nonlin Dyn. 27 211

    [19]

    Maccari A 2003 Int. J. Non-Lin Mech. 38 123

    [20]

    Maccari A 2003 J. Sound Vib. 259 241

    [21]

    Qi W, Zhang Y, Wang Y H 2009 Chin. Phys. B 18 1404

    [22]

    Shi P M, Han D Y, Liu B 2010 Chin. Phys. B 19 090306

    [23]

    Qian C Z, Tang J S 2006 Acta Phys. Sin. 55 617 (in Chinese) [钱长照、 唐驾时 2006 物理学报 55 617]

    [24]

    Nayfeh A H 1981 Introduction to Perturbation Techniques (New York:Academic) p46

    [25]

    Shi P M, Liu B, Jiang J S 2009 Acta Phys. Sin. 58 2147 (in Chinese) [时培明、 刘 彬、 蒋金水 2009 物理学报 58 2147]

  • [1]

    Carmeli M 1985 Found. Phys. 15 175

    [2]

    Carmeli M 1986 Inter. J. Theor. Phys. 15 89

    [3]

    Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]

    [4]

    Luo S K 1998 Appl. Math. Mech. 19 45

    [5]

    Fu J L, Chen X W, Luo S K 1999 Appl. Math. Mech. 20 1266

    [6]

    Fu J L, Chen X W, Luo S K 2000 Appl. Math. Mech. 21 549

    [7]

    Luo S K, Guo Y X, Chen X W 2001 Acta Phys. Sin. 50 2053 (in Chinese) [罗绍凯、 郭永新、 陈向炜 2001 物理学报 50 2053]

    [8]

    Luo S K 2002 Chin. Phys. Lett . 19 449

    [9]

    Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523

    [10]

    Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004物理学报 53 5]

    [11]

    Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271

    [12]

    Fang J H 2000 Acta Phys. Sin. 49 1028 (in Chinese) [方建会 2000 物理学报 49 1028]

    [13]

    Jia L Q 2003 Acta Phys. Sin. 52 1039 (in Chinese) [贾利群 2003 物理学报 52 1039]

    [14]

    Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林、 刘 彬 2002 物理学报 51 2191]

    [15]

    Shi P M, Liu B, Hou D X 2008 Acta Phys. Sin. 57 1321 (in Chinese) [时培明、 刘 彬、 侯东晓 2008 物理学报 57 1321]

    [16]

    Shi P M, Liu B,Hou D X 2009 Chinese Journal of Mechanical Engineering 22 132

    [17]

    Belhaq M, Guennoun K, Houssni M 2002 Int. J. Non-Lin Mech. 37 445

    [18]

    Guennoun K, Belhaq M, Houssni M 2002 Nonlin Dyn. 27 211

    [19]

    Maccari A 2003 Int. J. Non-Lin Mech. 38 123

    [20]

    Maccari A 2003 J. Sound Vib. 259 241

    [21]

    Qi W, Zhang Y, Wang Y H 2009 Chin. Phys. B 18 1404

    [22]

    Shi P M, Han D Y, Liu B 2010 Chin. Phys. B 19 090306

    [23]

    Qian C Z, Tang J S 2006 Acta Phys. Sin. 55 617 (in Chinese) [钱长照、 唐驾时 2006 物理学报 55 617]

    [24]

    Nayfeh A H 1981 Introduction to Perturbation Techniques (New York:Academic) p46

    [25]

    Shi P M, Liu B, Jiang J S 2009 Acta Phys. Sin. 58 2147 (in Chinese) [时培明、 刘 彬、 蒋金水 2009 物理学报 58 2147]

计量
  • 文章访问数:  7952
  • PDF下载量:  872
  • 被引次数: 0
出版历程
  • 收稿日期:  2010-09-19
  • 修回日期:  2010-12-20
  • 刊出日期:  2011-09-15

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