Periodic sticking motion in a two-degree-of-freedom impact oscillator

International Journal of Non-Linear Mechanics

Volumn 40, Issue 8, 2005, Pages 1076-1087

  Wagg, D J ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

2DOF Oscillator; Impact; Multi sliding; Periodic; Sticking

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; CONSTRAINT THEORY; DEGREES OF FREEDOM (MECHANICS); FREQUENCY MODULATION; MATHEMATICAL MODELS; MOTION ESTIMATION; TIME VARYING SYSTEMS;

2DOF OSCILLATORS; IMPACT; MULTI-SLIDING; PERIODIC; STICKING;

OSCILLATIONS;

EID: 23344439822     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2005.03.002     Document Type: Article

References (35)

1. D.J. Wagg, and S.R. Bishop Dynamics of a two degree of freedom vibro-impact system with multiple motion limiting constraints Int. J. Bifurcation Chaos 14 1 2004 119 140
2. S.F. Masri Theory of the dynamic vibration neutraliser with motion-limiting stops Trans. Am. Soc. Mech. Eng. J. Appl. Mech. 39 1972 563 568
3. F.C. Moon, and S.W. Shaw Chaotic vibrations of a beam with non-linear boundary conditions Int. J. Non-Linear Mech. 18 6 1983 465 477
4. S. Chatterjee, A.K. Mallik, and A. Ghosh On impact dampers for non-linear vibrating systems J. Sound Vib. 187 3 1995 403 420
5. C.N. Bapat The general motion of an inclined impact damper with friction J. Sound Vib. 184 3 1995 417 427
6. B. Blazejczyk-Okolewska Analysis of an impact damper of vibrations Chaos, Solitions Fractals 12 2001 1983 1988
7. S.E. Semercigil, F. Collette, and D. Huyni Experiments with tuned absorber - impact damper combination J. Sound Vib. 256 1 2002 179 188
8. M.F.A. Azeez, and A.F. Vakakis Numerical and experimental analysis of a continuous overhung rotor undergoing vibro-impacts Int. J. Non-Linear Mech. 34 1999 415 435
9. P. Metallidis, and S. Natsiavas Vibration of a continuous system with clearance and motion constraints Int. J. Non-Linear Mech. 35 2000 675 690
10. J. Shaw, and S.W. Shaw The onset of chaos in a two-degree of freedom impacting system J. Appl. Mech. 56 1989 168 174
11. G.W. Luo, and J.H. Xie Hopf bifurcation of a two-degree-of-freedom vibro-impact system J. Sound Vib. 213 1998 391 408
12. G.-L. Wen Codimension-2 hopf bifurcation of a two-degree-of-freedom vibro-impact system J. Sound Vib. 242 3 2001 475 485
13. G.W. Luo, and J.H. Xie Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases Non-linear Mech. 37 2002 19 34
14. S.J. Hogan, and M.E. Homer Graph theory and piecewise smooth dynamical systems of arbitary dimension Chaos, Solitons & Fractals 10 11 1999 1869 1880
15. S. Lenci, and G. Rega Regular nonlinear dynamics and bifurcations of an impacting system under general periodic excitation Nonlinear Dyn. 34 2004 249 268
16. A.X.C.N. Valente, N.H. McClamroch, and I. Mezic Hybrid dynamics of two coupled oscillators that can impact a fixed stop Int. J. Non-Linear Mech. 38 2003 677 689
17. S. Theodossiades, and S. Natsiavas Periodic and chaotic dynamics of motor-driven gear-pair system with backlash Chaos, Solitons Fractals 12 2001 2427 2440
18. J.P. Cusumano, and B.-Y. Bai Period-infinity periodic motions, chaos and spatial coherence in a 10 degree of freedom impact oscillator Chaos, Solitons and Fractals 3 1993 515 536
19. M.M. Nigm, and A.A. Shabana Effect of an impact damper on a multi-degree of freedom system J. Sound Vib. 89 4 1983 541 557
20. F. Pfeiffer, and C. Glocker Multibody Dynamics with Unilateral Contacts 1996 Wiley New York
21. S. Natsiavas Dynamics of multiple-degree-of-freedom oscillators with colliding components J. Sound Vib. 165 3 1993 439 453
22. D. Pun, S.L. Lua, S.S. Law, and D.Q. Cao Forced vibration of a multidegree impact oscillator J. Sound Vib. 213 3 1998 447 466
23. C.J. Budd, and F. Dux Chattering and related behaviour in impact oscillators Philos. Trans. R. Soc. London A 347 1994 365 389
24. A.B. Nordmark, R.E.M. Kisitu, On chattering bifurcations in 1dof impact oscillator models, Royal Institute of Technology, Sweden, 2003, preprint.
25. D.J. Wagg, and S.R. Bishop Chatter, sticking and chaotic impacting motion in a two-degree of freedom impact oscillator Int. J. Bifurcation Chaos 11 1 2001 57 71
26. C.N. Bapat Periodic motions of an impact oscillator J. Sound Vib. 209 1 1998 43 60
27. C. Toulemonde, and C. Gontier Sticking motions of impact oscillators Eur. J. Mech. A: Solids 17 2 1998 339 366
28. D.J. Wagg Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator Chaos, Solitions and Fractals 22 3 2004 541 548
29. M. Di Bernardo, K.H. Johansson, and F. Vasca Self-oscillations and sliding in relay feedback systems: symmetry and bifurcations Int. J. Bifurcation Chaos 4 11 2001 1121 1140
30. P. Kowalczyk, M. di Bernardo, On a novel class of bifurcations in hybrid dynamical systems, in: Lecture Notes in Computer Science, vol. 2034, 2001, pp. 361-374.
31. M. Di Bernardo, P. Kowalczyk, and A. Nordmark Bifurcations of dynamical systems with sliding: derivation of normal-form mappings Physica D 170 2002 175 205
32. S.P. Timoshenko Vibration Problems in Engineering 1937 Van Nostrand Princeton, NJ
33. J.M.T. Thompson, and H.B. Stewart Nonlinear Dynamics and Chaos 2002 Wiley Chichester
34. S.W. Shaw, and P.J. Holmes A periodically forced piecewise linear oscillator J. Sound Vib. 90 1 1983 129 155
35. M. Di Bernardo, P. Kowalczyk, and A. Nordmark Sliding bifurcations: a novel mechanism for the onset of chaos in dry friction oscillators Int. J. Bifurcation Chaos 13 10 2003 2935 2948