Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator

Chaos, Solitons and Fractals

Volumn 19, Issue 4, 2004, Pages 823-839

  Luo, Albert C J ^a  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); INTEGRATION; SOLITONS;

HORIZONTAL IMPACT OSCILLATORS;

CHAOS THEORY;

EID: 0042623544     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00195-4     Document Type: Article

References (31)

1. Han R.P.S., Luo A.C.J., Deng W. Chaotic motion of a horizontal impact pair. Journal of Sound and Vibration. 181:1995;231-250.
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):1990;414-432.
3. Luo A.C.J. An unsymmetrical motion in a horizontal impact oscillator. ASME Journal of Vibration and Acoustics. 124:2002;420-426.
4. Deng W. Action of the impact damper and determination of its basic parameters. Chinese Journal of Mechanical Engineering. 12:1964;83-93.
5. Masri S.F., Caughey T.D. On the stability of the impact damper. ASME Journal of Applied Mechanics. 33:1966;586-592.
6. Masri S.F. General motion of impact dampers. Journal of the Acoustical Society of America. 47:1970;229-237.
7. Senator M. Existence and stability of periodic motions of a harmonically forced impacting system. Journal of Acoustics Society of America. 47:1970;1390-1397.
8. Bapat C.N., Popplewell N., Mclachlan K. Stable periodic motion of an impact pair. Journal of Sound and Vibration. 87:1983;19-40.
9. Bapat C.N., Sankar S. Single unit impact damper in free and forced vibrations. Journal of Sound and Vibration. 99:1985;85-94.
10. Bapat C.N., Bapat C. Impact-pair under periodic excitation. Journal of Sound and Vibration. 120:1988;53-61.
11. Shaw S.W., Holmes P.J. A periodically forced piecewise linear oscillator. ASME Journal of Applied Mechanics. 50:1983;129-155.
12. Shaw S.W., Holmes P.J. A periodically forced impact oscillator. Journal of Sound and Vibration. 90:1983;129-155.
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. 52:1985;453-458.
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. 52:1985;459-464.
15. Whiston G.S. Global dynamics of vibro-impacting linear oscillator. Journal of Sound and Vibration. 118:1987;395-429.
16. Whiston G.S. Global dynamics of vibro-impacting linear oscillator. Journal of Sound and Vibration. 152:1992;395-429.
17. Nordmark A.B. Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound and Vibration. 145:1991;279-297.
18. Foale S., Bishop S.R. Dynamical complexities of forced impacting systems. Philosophy Transactions of the Royal Society London A. 338:1992;547-556.
19. Foale S. Analytical determination of bifurcation in an impact oscillator. Philosophy Transactions of the Royal Society London A. 347:1994;353-364.
20. Budd C., Dux F. Chattering and related behavior in impact oscillator. Proceedings of the Royal Society London A. 347:1994;365-389.
21. Budd C.J., Lee A.G. Double impact orbits of periodically forced impact oscillator. Proceedings of the Royal Society London A. 452:1996;2719-2750.
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. 452:1996;2579-2592.
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. 9:1998;261-269.
24. 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. 10:1996;1-18.
26. Hogan S.J., Homer M.E. Graph theory and piecewise smooth dynamical systems of arbitrary dimension. Chaos, Solitons & Fractals. 10:1999;1869-1880.
27. Nusse H.E., Ott E., Yorke J.A. Border-collision bifurcations: An expantion for observed bifurcation phenomena. Physical Review E. 49:1994;1073-1076.
28. Chin W., Ott E., Nusse H.E., Grebogi C. Grazing bifurcation in impact oscillator. Physical Review E. 50:1994;4427-4444.
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. 45:1998;707-715.
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. 47:2000;389-394.
31. Dankowicz H., Nordmark A.B. On the origin and bifurcations of stick-slip oscillations. Physica D. 136:2000;280-302.