×

Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator. (English) Zbl 1135.37306

Stability and bifurcations for the LR-model motion in a horizontal impact oscillator is determined analytically and numerically. The regions for such conditions in parameter space are developed. The chaotic motion induced by the period-doubling bifurcation on the LR model is investigated numerically.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Han, R. P.S.; Luo, A. C.J.; Deng, W., Chaotic motion of a horizontal impact pair, Journal of Sound and Vibration, 181, 231-250 (1995) · Zbl 1237.70028
[2] Li, G. X.; Rand, R. H.; Moon, F. C., Bifurcation and Chaos in a forced zero-stiffness impact oscillator, International Journal of Nonlinear Mechanics, 25, 4, 414-432 (1990) · Zbl 0714.73049
[3] Luo, A. C.J., An unsymmetrical motion in a horizontal impact oscillator, ASME Journal of Vibration and Acoustics, 124, 420-426 (2002)
[4] Deng, W., Action of the impact damper and determination of its basic parameters, Chinese Journal of Mechanical Engineering, 12, 83-93 (1964)
[5] Masri, S. F.; Caughey, T. D., On the stability of the impact damper, ASME Journal of Applied Mechanics, 33, 586-592 (1966)
[6] Masri, S. F., General motion of impact dampers, Journal of the Acoustical Society of America, 47, 229-237 (1970)
[7] Senator, M., Existence and stability of periodic motions of a harmonically forced impacting system, Journal of Acoustics Society of America, 47, 1390-1397 (1970)
[8] Bapat, C. N.; Popplewell, N.; Mclachlan, K., Stable periodic motion of an impact pair, Journal of Sound and Vibration, 87, 19-40 (1983) · Zbl 0556.70019
[9] Bapat, C. N.; Sankar, S., Single unit impact damper in free and forced vibrations, Journal of Sound and Vibration, 99, 85-94 (1985)
[10] Bapat, C. N.; Bapat, C., Impact-pair under periodic excitation, Journal of Sound and Vibration, 120, 53-61 (1988)
[11] Shaw, S. W.; Holmes, P. J., A periodically forced piecewise linear oscillator, ASME Journal of Applied Mechanics, 50, 129-155 (1983) · Zbl 0561.70022
[12] Shaw, S. W.; Holmes, P. J., A periodically forced impact oscillator, Journal of Sound and Vibration, 90, 129-155 (1983) · Zbl 0561.70022
[13] Shaw, S. W., Dynamics of harmonically excited systems having rigid amplitude constraints. Part I-subharmonic motions and local bifurcations, ASME Journal of Applied Mechanics, 52, 453-458 (1985)
[14] Shaw, S. W., Dynamics of harmonically excited systems having rigid amplitude constraints. Part II-chaotic motions and global bifurcations, ASME Journal of Applied Mechanics, 52, 459-464 (1985)
[15] Whiston, G. S., Global dynamics of vibro-impacting linear oscillator, Journal of Sound and Vibration, 118, 395-429 (1987) · Zbl 1235.70209
[16] Whiston, G. S., Global dynamics of vibro-impacting linear oscillator, Journal of Sound and Vibration, 152, 395-429 (1992) · Zbl 1235.70209
[17] Nordmark, A. B., Non-periodic motion caused by grazing incidence in an impact oscillator, Journal of Sound and Vibration, 145, 279-297 (1991)
[18] Foale, S.; Bishop, S. R., Dynamical complexities of forced impacting systems, Philosophy Transactions of the Royal Society London A, 338, 547-556 (1992) · Zbl 0748.70011
[19] Foale, S., Analytical determination of bifurcation in an impact oscillator, Philosophy Transactions of the Royal Society London A, 347, 353-364 (1994) · Zbl 0813.70012
[20] Budd, C.; Dux, F., Chattering and related behavior in impact oscillator, Proceedings of the Royal Society London A, 347, 365-389 (1994) · Zbl 0816.70018
[21] Budd, C. J.; Lee, A. G., Double impact orbits of periodically forced impact oscillator, Proceedings of the Royal Society London A, 452, 2719-2750 (1996) · Zbl 0885.70019
[22] Bishop, S. R.; Thompson, M. G.; Faole, S., Prediction of period-1 impact in a driven beam, Proceedings of the Royal Society London A, 452, 2579-2592 (1996)
[23] Bishop, S. R.; Wagg, D. J.; Xu, D., Use of control to maintain period-1 motion during wind-up or wind-down operations of an impacting driven beam, Chaos, Solitons & Fractals, 9, 261-269 (1998)
[24] Luo ACJ. Analytical Modeling of Bifurcations, Chaos and Fractals in Nonlinear Dynamics PhD Dissertation, University of Manitoba, Winnipeg, Canada, 1995; Luo ACJ. Analytical Modeling of Bifurcations, Chaos and Fractals in Nonlinear Dynamics PhD Dissertation, University of Manitoba, Winnipeg, Canada, 1995
[25] Luo, A. C.J.; Han, R. P.S., Dynamics of a bouncing ball with a periodic vibrating table revisited, Nonlinear Dynamics, 10, 1-18 (1996)
[26] Hogan, S. J.; Homer, M. E., Graph theory and piecewise smooth dynamical systems of arbitrary dimension, Chaos, Solitons & Fractals, 10, 1869-1880 (1999) · Zbl 0955.37009
[27] Nusse, H. E.; Ott, E.; Yorke, J. A., Border-collision bifurcations: An expantion for observed bifurcation phenomena, Physical Review E, 49, 1073-1076 (1994)
[28] Chin, W.; Ott, E.; Nusse, H. E.; Grebogi, C., Grazing bifurcation in impact oscillator, Physical Review E, 50, 4427-4444 (1994)
[29] Yuan, G.; Banerjee, S.; Ott, E.; Yorke, J. A., Border-collision bifurcation in the buck converter, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 45, 707-715 (1998) · Zbl 0952.94020
[30] Banerjee, S.; Karthik, M. S.; Yuan, G.; Yorke, J. A., Bifurcations in one-dimensional piecewise smooth maps-theory and applications in switching circuits, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 47, 389-394 (2000) · Zbl 0968.37013
[31] Dankowicz, H.; Nordmark, A. B., On the origin and bifurcations of stick-slip oscillations, Physica D, 136, 280-302 (2000) · Zbl 0963.70016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.