Phase-Space Reconstructions and Stick-Slip

Nonlinear Dynamics

Volumn 13, Issue 1, 1997, Pages 39-57

  Feeny, B F ^a   Liang, J W ^b  

^a Michigan State University   (United States)

^b MING CHI UNIVERSITY OF TECHNOLOGY   (Taiwan)

Author keywords

Friction oscillators; Method of delays; Nonsmooth systems; Phase space reconstructions; Stick slip

Indexed keywords

CHAOS THEORY; DEGREES OF FREEDOM (MECHANICS); OSCILLATORS (MECHANICAL); PHASE SPACE METHODS;

FRICTION OSCILLATORS; METHOD OF DELAYS; NONSMOOTH SYSTEMS; PHASE-SPACE RECONSTRUCTIONS; STICK-SLIP PROCESS;

STATE ESTIMATION;

EID: 0031142828     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008245332549     Document Type: Article

References (28)

1. Kennel, M., Brown, R., and Abarbanel, H. D. I., 'Determining embedding dimension for phase-space reconstruction using a geometrical construction', Physical Review A 45, 1992, 3403-3411.
2. Abarbanel, H. D. I., Brown, R., Sidorowich, J., and Tsimring, L., 'The analysis of observed chaotic data in physical systems', Reviews of Modern Physics 65, 1993, 1331-1392.
3. Takens, F., 'Detecting strange attractors in turbulence', in Dynamical Systems and Turbulence, D. A. Rand and L. S. Young (eds.), Lecture Notes in Math., Vol. 898, Springer, 1981, pp. 366-381.
4. Feeny, B., 'The nonlinear dynamics of oscillators with stick-slip friction', in Dynamics with Friction, A. Guran, F. Pfeiffer, and K. Popp (eds.), World Scientific, 1996, pp. 36-92.
5. Feeny, B., 'A nonsmooth Coulomb friction oscillator', Physica D 59, 1992, 25-38.
6. Popp, K. and Stelter, P., 'Stick-slip vibrations and chaos', Philosophical Transactions of the Royal Society of London A 332, 1990, 89-105.
7. Marui, E. and Kato, S., 'Forced vibration of a base-excited single-degree-of-freedom system with Coulomb friction', Journal of Dynamic Systems, Measurement, and Control 106, 1984, 280-285.
8. Polycarpou, A., and Soom, A., 'Transitions between sticking and slipping at lubricated line contacts', in Friction-Induced Vibration, Chatter, Squeal, and Chaos, ASME Winter Annual Meeting, DE-Vol. 49, 1992, pp. 139-148.
9. Pratap, R., Mukherjee, S., and Moon, F. C., 'Dynamic behavior of a bilinear hysteretic elasto-plastic oscillator, parts I and II', Journal of Sound and Vibration 172, 1994, 321-358.
10. Utkin, V. I., 'Variable-structure systems with sliding mode control', IEEE Transactions on Automatic Control 22, 1973, 212-222.
11. Kowalik, Z. J., Franaszek, M., and Pieránski, P., 'Self-reanimating chaos in the bouncing-ball system', Physical Review A 37, 1988, 4016-4022.
12. Cusumano, J. P. and Bai, B.-Y., 'Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree-of-freedom impact oscillator', Chaos, Solitons and Fractals 3(5), 1993, 515-535.
13. Moon, F. C., 'Chaotic vibrations of a magnet near a superconductor', Physics Letters A 132(5), 1988, 249-252.
14. Feeny, B. and Moon, F. C., 'Autocorrelation on symbol dynamics for a chaotic dry-friction oscillator', Physics Letters A 141(8-9), 1989, 397-400.
15. Feeny, B. and Moon, F. C., 'Chaos in a dry-friction oscillator: experiment and numerical modeling', Journal of Sound and Vibration 170, 1994, 303-323.
16. Anderson, J. R. and Ferri, A. A., 'Behavior of a single-degree-of-freedom system with a generalized friction law', Journal of Sound and Vibration 140(2), 1990, 287-304.
17. Shaw, S. W., 'On the dynamic response of a system with dry friction', Journal of Sound and Vibration 108, 1986, 305-325.
18. Fraser, A. M., 'Reconstructing attractors from scalar time series: A comparison of singular system analysis and redundancy criteria', Physica D 34, 1989, 391-404.
19. Broomhead, D. S. and King, G. P., 'Extracting qualitative dynamics from experimental data', Physica D 20, 1986, 217-236.
20. Popp, K., Hinrichs, N., and Oestreich, M., 'Analysis of a self-excited friction oscillator with external excitation', in Dynamics with Friction, A. Guran, F. Pfeiffer, and K. Popp (eds.), World Scientific, 1995, pp. 1-35.
21. Auerbach, D., Cvitanovic, P., Eckmann, J.-P., Gunaratne, G., and Procaccia, I., 'Exploring chaotic notion through periodic orbits', Physical Review Letters 58, 1987, 2387-2389.
22. Lathrop, D. P. and Kostelich, E. J., 'Characterization of an experimental strange attractor by periodic orbits', Physical Review A 40, 1987, 4028-4031.
23. Tufillaro, N. B., Abbott, T., and Reilly, J., An Experimental Approach to Nonlinear Dynamics and Chaos, Addison-Wesley, New York, 1992.
24. Feeny, B. F. and Liang, J. W., 'Phase-space reconstructions of stick-slip systems', in Proceedings of the ASME 1995 Design Engineering Technical Conferences, 3A, ASME DE-Vol. 84-1, 1995, 1061-1070.
25. Read, P. L., 'Phase portrait reconstruction using multivariate singular systems analysis', Physica D 69, 1993, 353-365.
26. Holmes, P. and Ghrist, R., 'Knotting within the gluing bifurcation', in Nonlinearity and Chaos in Engineering Dynamics, J. M. T. Thompson and S. R. Bishop (eds.), Wiley, Chichester, 1994, pp. 299-315.
27. Tufillaro, N. B., Solari, H. G., and Gilmore, R., 'Relative rotation rates - fingerprints for strange attractors', Physical Review A 41, 1990, 5717-5720.
28. Carlson, J. M. and Langer, J. S., 'Mechanical model of an earthquake fault', Physical Review A 40(11), 1989, 6470-6484.