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A kind of one-degree-of-freedom nonlinear moving belt system is considered. The analytical research of sliding region and existence conditions of equilibrium are first derived by the theory of piecewise-smooth dynamical system. Then, using numerical method, one- or two-parameter continuation of several types of periodic orbits of the system is calculated. We obtain codimension-1 sliding bifurcation curves, codimension-2 sliding bifurcation points, and global bifurcation diagram in parameter space for the system. The investigation of bifurcation behavior shows that the speed of moving belt and amplitude of friction have a great influence on dynamic behavior, and reveals the complex nonlinear dynamic phenomenon of the moving belt system.
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Keywords:
- moving belt system /
- sliding bifurcation /
- periodic motion
[1] Galvanetto U, Bishop S R 1994 Int. J. Mech. Sci. 36 683
[2] Galvanetto U, Bishop S R 1995 Chaos Soliton. Fract. 5 2171
[3] Filippov A F 1988 Differential Equations With Discontinuous Righthand Side (Dordrecht: Kluwer Academic Publishers)
[4] Li Q H, Yan Y L, Yang D 2012 Acta Phys. Sin. 61 200505 (in Chinese) [李群宏, 闫玉龙, 杨丹 2012 物理学报 61 200505]
[5] Galvanetto U 2001 J. Sound Vib. 248 653
[6] Dankowicz H, Nordmark A B 2000 Physica D 136 280
[7] Bernardo M, Kowalczyk P, Nordmark A 2002 Physica D 170 175
[8] Li Q H, Chen Y M, Qin Z Y 2011 Chin. Phys. Lett. 28 030502
[9] Luo A C J, Gegg B C 2006 J. Sound Vib. 291 132
[10] Hetzler H, Schwarzer D, Seemann W 2007 Commun. Nonlinear Sci. Numer. Simulat. 12 83
[11] Kowalczyk P, di Bernardo M 2005 Physica D 204 204
[12] Dercole F, Kuznetsov Y A 2005 ACM T. Math. Software 31 95
[13] Kowalczyk P, Piiroinen P T 2008 Physica D 237 1053
[14] Guardia M, Hogan S J, Seara T M 2010 SIAM J. Appl. Dyn. Syst. 9 769
[15] Luo A C J, Huang J 2012 Nonlinear Anal. Real. 13 241
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[1] Galvanetto U, Bishop S R 1994 Int. J. Mech. Sci. 36 683
[2] Galvanetto U, Bishop S R 1995 Chaos Soliton. Fract. 5 2171
[3] Filippov A F 1988 Differential Equations With Discontinuous Righthand Side (Dordrecht: Kluwer Academic Publishers)
[4] Li Q H, Yan Y L, Yang D 2012 Acta Phys. Sin. 61 200505 (in Chinese) [李群宏, 闫玉龙, 杨丹 2012 物理学报 61 200505]
[5] Galvanetto U 2001 J. Sound Vib. 248 653
[6] Dankowicz H, Nordmark A B 2000 Physica D 136 280
[7] Bernardo M, Kowalczyk P, Nordmark A 2002 Physica D 170 175
[8] Li Q H, Chen Y M, Qin Z Y 2011 Chin. Phys. Lett. 28 030502
[9] Luo A C J, Gegg B C 2006 J. Sound Vib. 291 132
[10] Hetzler H, Schwarzer D, Seemann W 2007 Commun. Nonlinear Sci. Numer. Simulat. 12 83
[11] Kowalczyk P, di Bernardo M 2005 Physica D 204 204
[12] Dercole F, Kuznetsov Y A 2005 ACM T. Math. Software 31 95
[13] Kowalczyk P, Piiroinen P T 2008 Physica D 237 1053
[14] Guardia M, Hogan S J, Seara T M 2010 SIAM J. Appl. Dyn. Syst. 9 769
[15] Luo A C J, Huang J 2012 Nonlinear Anal. Real. 13 241
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