Summary
Friction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. On the basis of a one-dimensional map, the bifurcation behaviour including unstable branches is investigated for a friction oscillator with simultaneous self-and external excitation. The chosen way of mapping also allows a simple determination of Lyapunov exponents.
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References
ACSL Advanced Continuous Simulation Language: Reference Manual. Edition 10.0, Mitchell and Gauthier Associates, 1991
Guckenheimer, J.;Holmes, P.: Nonlinear oscillations, dynamical systems, and bifurcation of vector fields. New York: Springer 1983
Hale, J.;Kocak, H.: Dynamics and bifurcations. Berlin: Springer 1991
Hilborn, R. C.: Chaos and nonlinear dynamics. Oxford: Oxford University Press 1994
Leven, R. W.;Koch, B.-P.;Pompe, B.: Chaos in dissipativen Systemen. Berlin: Akademie-Verlag 1989
Manneville, P.;Pomeau, Y.: Different ways to turbulence in dissipative dynamical systems. Physica 1D (1980) 219–226
Moon, F. C.: Chaotic and fractal dynamics. New York: John Wiley 1992
Müller, A.;Hubbuch, F.: Lyapunov Exponenten in nicht-glatten dynamischen Systemen. ZAMM 75 (1995) 91–92
Müller, P. C.: Calculation of Lyapunov exponents for dynamic systems with discontinuities. Journal of Chaos, Solitons and Fractals 5 (1995), No. 9, 1671–1681
Popp, K.: Chaostiche Bewegungen beim Reibschwinger mit simultaner Selbst- und Fremderregung. ZAMM 71 (1991) 71–73
Popp, K.;Hinrichs, N.;Oestreich, M.: Dynamical behavior of a friction oscillator with simultaneous self and external excitation. Sadhana 20 (1995), Part 2-4, 627–654
Popp, K.;Hinrichs, N.;Oestreich, M.: Numerische Untersuchung von Stick-Slip-Bewegungen mit Hilfe geglätteter Reibkennlinien. ZAMM 75 (1995) 63–64
Popp, K.;Stelter, P.: Nonlinear oscillations of structures induced by dry friction. In: Schiehlen, W. (ed.) Nonlinear dynamics in engineering systems, pp. 233–240. Berlin: Springer 1990
Popp, K.; Stelter, P.: Stick-slip vibrations and chaos. Phil. Trans. R. Soc. London/A (1990) 89–105
Seydel, R.: From equilibrium to chaos. Amsterdam: Elsevier 1988
Seydel, R.: BIFPACK—A program package for continuation, bifurcation and stability analysis. Mathematische Institute der Julius-Maximilians-Universität Würzburg, Version 2.4, 1993
Stelter, P. Nichtlineare Schwingungen reibungserregter Strukturen. VDI Reihe 11 Nr. 137. Düsseldorf: VDI-Verlag 1990
Stelter, P.: Nonlinear vibrations of structures induced by dry friction. Nonlinear Dyn. 3 (1992) 329–345
Stelter, P.; Popp, K.: Chaotic behaviour of structures excited by dry friction forces. Proc. Workshop on Rolling Noise Generation, Berlin, 1989
Stelter, P.;Sextro, W.: Bifurcations in dynamic systems with dry friction. Int. Ser. Num. Math. 97 (1991) 343–347
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Dedicated to Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. mult. Erwin Stein on the occasion of his 65th birthday.
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Oestreich, M., Hinrichs, N. & Popp, K. Bifurcation and stability analysis for a non-smooth friction oscillator. Arch. Appl. Mech. 66, 301–314 (1996). https://doi.org/10.1007/BF00795247
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DOI: https://doi.org/10.1007/BF00795247