On the existence of a stable periodic solution of an impacting oscillator with damping

Chaos, Solitons and Fractals

Volumn 19, Issue 5, 2004, Pages 1291-1311

  Czolczynski, Krzysztof ^a  

^a LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DAMPING; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; IMPACT TESTING;

CHAOTIC MOTION;

OSCILLATORS (MECHANICAL);

EID: 0141839038     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0960-0779(03)00336-9     Document Type: Article

References (33)

1. Aidanpaa J.O., Gupta R.B. Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system. J. Sound Vibrat. 165(2):1993;305-327.
2. Arnold RN. The acceleration absorber. In: Proceedings of International Conference of Applied Mechanics; 1956. p. 367-72.
3. Blazejczyk-Okolewska B. Analysis of an impact damper of vibration. Chaos, Solitons & Fractals. 12:2001;1983-1988.
4. Blazejczyk-Okolewska B., Czolczynski K. Some aspects of the dynamical behaviour of the impact force generator. Chaos, Solitons & Fractals. 9:1998;1307-1320.
5. Blazejczyk-Okolewska B., Czolczynski K. Impact oscillator as dynamic damper. Mech. Mech. Eng. 4(1):2000;105-112.
6. Blazejczyk-Okolewska B., Brindley J., Czolczynski K., Kapitaniak T. Antiphase synchronization of chaos by noncontinuous coupling: two impacting oscillators. Chaos, Solitons & Fractals. 12:2001;1823-1826.
7. Cempel C. The periodical vibration with impacts in mechanical discreet systems, Thesis no. 44. Poland: Technical University of Poznan, 1970.
8. Cempel C. Receptance model of the multi-unit vibration impact neutralizer "MUVIN" J. Sound Vibrat. 40:1975;249-266.
9. Chin W., Ott E., Nusse H.E., Grebogi C. Grazing bifurcations in impact oscillators. Phys. Rev. E. 50(6):1994;4427-4444.
10. Czolczynski K., Blazejczyk-Okolewska B. Dynamics of the linear oscillator with impacts. Mech. Mech. Eng. 3(1):1999;5-14.
11. Czolczynski K., Blazejczyk-Okolewska B. Dynamics of two independent impacting oscillators. Mach. Dynam. Problems. 24(1):2000;47-61.
12. Czolczynski K. On the existence of a stable periodic motion of two impacting oscillators. Chaos, Solitons & Fractals. 15:2003;371-379.
13. Czolczynski K., Kapitaniak T. Influence of the mass and stiffness ratio on a periodic motion. Chaos, Solitons & Fractals. 17:2003;1-10.
14. Egle DM. On investigation of an impact vibration absorber. Trans ASME, J Eng Ind November 1967: 653-61.
15. Goyda H., Teh C.A. A study of the impact dynamics of loosely supported heat exchanger tubes. ASME J. Pressure Tech. 111:1989;394-401.
16. Grubin C. On the theory of the acceleration damper. Trans ASME, J Appl Mech September 1956: 373-8.
17. Hinrichs N., Oestreich M., Popp K. Dynamics of oscillators with impact and friction. Chaos, Solitons & Fractals. 8:1997;535-558.
18. Isomaki H.M., Von Boehm J., Raty R. Devil's attractors and chaos of a driven impact oscillator. Phys. Lett. 107A(8):1985;343-346.
19. Kaharaman A., Singh R. Nonlinear dynamics of a spur gear pair. J. Sound Vibrat. 142:1990;49-75.
20. Masri SF, Caughey TK. On the stability of the impact damper. Trans ASME, J Appl Mech September 1966: 586-92.
21. Moon F.C. Chaotic vibrations. 1987;John Wiley, New York.
22. Nordmark A.B. Non-periodic motion caused by grazing incidence in an impact oscillator. J. Sound Vibrat. 145:1991;279-297.
23. Peterka F. An investigation of the motion of impact dampers: theory of the fundamental impact motion. Strojnicky Casopis. 21(5):1970;457-478.
24. Peterka F., Vacik J. Transition to chaotic motion in mechanical systems with impacts. J. Sound Vibrat. 154(1):1992;95-115.
25. Shaw S.W., Holmes P.J. A periodically forced impact oscillator with large dissipation. J. Appl. Mech. 50:1983;849-857.
26. Shaw S.W., Holmes P.J. A periodically forced piecewise linear oscillator. J. Sound Vibrat. 90:1983;129-155.
27. Shaw S.W. Dynamics of harmonically excited systems having rigid amplitude constraints. Part 1: subharmonic motions and local bifurcations. J. Appl. Mech. 52:1985;453-458.
28. Shaw S.W. Dynamics of harmonically excited systems having rigid amplitude constraints. Part 2. Chaotic motions and global bifurcations. J. Appl. Mech. 52:1985;459-464.
29. Shaw J., Shaw S.W. The onset of chaos in a two degree of freedom impacting system. J. Appl. Mech. 56:1989;168-174.
30. Thompson J.M.T., Ghaffari R. Chaos after period-doubling bifurcations in the resonance of an impact oscillator. Phys. Lett. 91A(1):1982;296-299.
31. Tung P.C., Shaw S.W. The dynamics of an impact print hammer. Vibrat. Stress Reliab. Des. 110:1988;193-199.
32. Whiston G.S. The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator. J. Sound Vibrat. 115:1987;303-319.
33. Whiston G.S. Global dynamics of a vibro-impacting linear oscillator. J. Sound Vibrat. 118:1987;395-429.