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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.
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Keywords:
- relatively rotation /
- quasic-periodic parametric excitation /
- time-delayed feedback /
- limit cycle
[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 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 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 49 1028]
[13] Jia L Q 2003 Acta Phys. Sin. 52 1039 (in Chinese) [贾利群 2003 52 1039]
[14] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林、 刘 彬 2002 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 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 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 58 2147]
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[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 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 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 49 1028]
[13] Jia L Q 2003 Acta Phys. Sin. 52 1039 (in Chinese) [贾利群 2003 52 1039]
[14] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林、 刘 彬 2002 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 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 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 58 2147]
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