Abstract
The dynamics of a simple dynamical system subjected to an elastic restoring force, viscous damping and dry friction forces is investigated. Self-sustained oscillations occur with non-standard attracting properties. Discontinuity of the governing equations leads to non-standard bifurcations, which are studied here, with analytical and numerical tools.
Similar content being viewed by others
References
Amontons, G., 'De le résistance causée dans les machines', Mémoires de l'Academie des Sciences (1699) 203–222.
Coulomb, C.A., 'Théorie des machines simples', Mémoires de Mathématique et de Physique de l'Academie des Sciences (1785) 161–331.
Burridge, R. and Knopoff, L., 'Model and theoretical seismicity', Bull. Seism. Soc. America 57 (1967) 341–371.
Nussbaum, J. and Ruina, A., 'A two degree-of-freedom earthquake model with static/dynamic friction', PAGEOPH 125 (1987) 629–656.
Carlson, J.M., and Langer, S., 'Mechanical model of an earthquake fault', Phys. Rev. A 40 (1989) 6470–6484.
Huang, J. and Turcotte, D.L., 'Evidence for chaotic fault interactions in the seismicity of the San Andreas fault and Nankai trough', Nature 348 (1990) 234–236.
Schelleng, J., 'The physics of the bowed string', Sci. Am. 230 (1974) 87–95.
McIntyre, M.E. and Woodhouse, J., 'On the fundamentals of bowed-string dynamics', Acoustica, 43 (1979) 109–120.
Ruina, A.L., 'Unsteady motions between sliding surfaces', Wear 113 (1986) 83–86.
Martins, J.A.C., Oden, J.T. and Simoes, F.M.F., 'A study of static and kinetic friction', Int. J. Eng. Sci. 28 (1990) 29–92.
Pfeiffer, F., 'On stick-slip vibrations in machine dynamics', Ing. Archiv. 54 (1992) 232–240.
Popp, K. and Stelter, P., 'Stick-slip vibrations and chaos', Phil. Trans. R. Soc. Lond A 332 (1990) 89–105.
Capone, G., D'Agostino, V., Della Valle, S. and Guida, D., 'Stick-slip instability analysis', Meccanica 27 (1992) 111–118.
Oestreich, M., Hinrichs, N. and Popp, K., 'Bifurcation and stability analysis for a non-smooth friction oscillator', Arch. Appl. Mech. 66 (1996) 301–314.
Hinrichs, N., Oestreich, M. and Popp, K., 'Dynamics of oscillators with impact and friction', Chaos Solitons and Fractals 8 (1997) 535–558.
Galvanetto, U., 'Bifurcations and chaos in a 4-dimensional stick-slip system', J. Sound and Vibration 204 (1997) 690–695.
Conti, P., 'Sulla resistenza di attrito', Rd. Acc. Lincei 11 (1875).
Meijard, J.P., 'Dynamics of Mechanical Systems', PhD Thesis, Technical University of Delft 1991.
Galvanetto, U. and Bishop, S.R., 'Computational techniques for nonlinear dynamics in multiple friction oscillators', Comp. Meth. Appl. Mech. Engng 163 (1998) 373–382.
Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Galvanetto, U., Bishop, S.R. Dynamics of a Simple Damped Oscillator Undergoing Stick-Slip Vibrations. Meccanica 34, 337–347 (1999). https://doi.org/10.1023/A:1004741715733
Issue Date:
DOI: https://doi.org/10.1023/A:1004741715733