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Dynamical behaviour of a friction oscillator with simultaneous self and external excitation

  • Advances in nonlinear structural dynamics
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Abstract

Friction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. In engineering applications these vibrations are undesirable and should be avoided. In the present paper it is shown how the very robust limit cycles of stick-slip vibrations can be broken up by a harmonic disturbance. Based on a simple model of a friction oscillator with simultaneous self and external excitation the resulting bifurcation behaviour and the routes to chaos are investigated for a wide range of system parameters. The influence of different types of friction characteristics is elaborated and the admissibility of smoothing procedures is examined by comparing results gained for non-smooth and smoothed friction characteristics.

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References

  • Abraham R H, Shaw C D 1982Dynamics — the geometry of behaviour. Part 1: Periodic behaviour (Santa Cruz: Aerial Press)

    Google Scholar 

  • Abraham R H, Shaw C D 1983Dynamics — the geometry of behaviour. Part 2: Chaotic behaviour (Santa Cruz: Aerial Press)

    Google Scholar 

  • ACSL (Advanced Continuous Simulation Language) 1991Reference manual. edn 10·0 (Concorde, MA: Mitchell & Gautheir)

    Google Scholar 

  • Bochet B 1961 Nouvelles Recherches Experimentelles sur le Frottement et Glissement.Mines Cabur 19: 27–120

    Google Scholar 

  • Conti P 1875 Sulla Resistanza die Attrito.Accad. Lincei 11 (16)

  • Devaney R L 1986An introducion to chaotic dynamical systems (Menlo Park, CA: Benjamin Cummings)

    Google Scholar 

  • Doedel F J 1981 AUTO: A program for the bifurcation analysis of autonomous system.Congr. Numer. 30: 265–285

    MathSciNet  Google Scholar 

  • Feeny B F, Moon F C 1993 Bifurcation sequences of a Coulomb friction oscillator.Nonlinear Dyn. 4: 25–37

    Google Scholar 

  • Fingberg U 1989 Squealing noise of railway wheels. A wheel-rail-squealing-noise model.Proc. Polish-German Workshop on Dyn. Problems in Mech. Syst., Madralin, Poland (Polska Akademia Nauk.) pp. 111–122

  • Fingberg U 1990 A model of wheel-rail squealing noise.J. Sound Vibr. 143: 365–377

    Article  Google Scholar 

  • Franke J 1882 Über die Abhängigkeit der gleitender Reibung von der Geschwindigkeit.Civ. Ing.

  • Galton I 1878 The action of brakes. On the effect of brakes upon railway trains.Engineering 25: 469–472

    Google Scholar 

  • Grabec I 1988 Explanation of random vibrations in cutting on grounds of deterministic chaos.Robotics and Computer-Integrated Manufacturing 14: 129–134

    Article  Google Scholar 

  • Guckenheimer J, Holmes P 1983Nonlinear oscillations, dynamical systems, and bifurcation of vector fields (New York, Berlin, Heidelberg: Springer-Verlag)

    Google Scholar 

  • Hagedorn P 1984 Nichtlineare Schwingungen.Wiesbaden: Akademische Verlagsgesellschaft

  • Hale J, Kocak H 1991Dynamics and bifurcations (Berlin, Heidelberg, New York: Springer-Verlag)

    MATH  Google Scholar 

  • Jahnke M 1987Nichtlineare Dynamik eines Reibschwingers. IfM, Diplomarbeit, Universität Hannover

  • Kaas-Petersen C 1987PATH-User’s Guide (Leeds: University of Leeds)

    Google Scholar 

  • Kauderer H 1958Nichtlineare Mechanik (Berlin: Springer-Verlag)

    MATH  Google Scholar 

  • Kraft K 1967 Der Einfluß der Fahrgeschwindigkeit auf den Haftwert zwischen Rad und Schiene.Archiv für Eisenbahntechnik 22: 58–67

    Google Scholar 

  • Kunick A, Steeb W H 1986Chaos in dynamischen Systemen (Mannheim, BI)

  • Leven R W, Koch B P, Pompe B 1982Chaos is dissipativen Systemen (Berlin: Akademie-Verlag)

    Google Scholar 

  • Magnus K 1961Schwingungen (Stuttgart: Teubner)

    MATH  Google Scholar 

  • Manneville P, Pomeau Y 1980 Intermittent transition to turbulence in dissipative dynamical systems.Commun. Math Phys. 74: 189–197

    Article  MathSciNet  Google Scholar 

  • Moon F C 1987Chaotic vibrations (New York: John Wiley & Sons)

    MATH  Google Scholar 

  • Moon F C 1992Chaotic and fractal dynamics (New York: John Wiley & Sons)

    Google Scholar 

  • Neimark J J, Landa P S 1987Stochastic and chaotic vibrations (Moscow: Nauka) (in Russian)

    Google Scholar 

  • Parlitz U, Lauterborn W 1987 Period-doubling cascades and devil’s staircases of the driven van der Pol oscillator.Phys. Rev. A36: 1428–1434

    Google Scholar 

  • Popp K 1991 Chaotische Bewegungen beim Reibschwinger mit simultaner Selbstund Fremderregung.Z. Angew. Math. Mech. 71: T71-T73

    Article  Google Scholar 

  • Popp K 1992 Some model problems showing stick-slip motion and chaos.Trans. ASME Friction-induced Vib., Chatter, Squeal Chaos DE-49: 1–12

    Google Scholar 

  • Popp K, Stelter P 1990a Nonlinear oscillations of structures induced by dry friction. InProceedings of IU T AM Symposium on nonlinear dynamics in engineering systems. (Berlin: Springer-Verlag) pp. 233–240

    Google Scholar 

  • Popp K, Stelter P 1990b Stick-slip vibrations and chaos.Philos. Trans. R. Soc. London A: 89–105

  • Popp K, Schneider E, Irretier H 1985 Noise generation in railway wheels due to rail-wheel contact forces.Proc. 9th IAVSD-Symp., Linkoping, pp. 448–466

  • Seydel R 1983From equilibrium to chaos; practical bifurcation and stability analysis (Amsterdam: Elsevier)

    Google Scholar 

  • Seydel R 1993 BIFPACK — A program package for continuation, bifurcation and stability analysis. Mathematische Institute der Julius-Maximilians-Universität Würzburg, Version 2·4

  • Sparrow C 1982The Lorenz equation: bifurcations, chaos, and strange attractors. Applied Mathematical Sciences 41 (New York: Springer-Verlag)

    Google Scholar 

  • Stelter P 1990Nichtlineare Schwingungen reibungserregter Strukturen. VDI R. 11 Nr. 137, Düsseldorf

  • Stelter P 1992 Nonlinear vibrations of structures induced by dry friction.Nonlinear Dyn. 3: 329–345

    Article  Google Scholar 

  • Stelter P, Popp K 1989 Chaotic behaviour of structures excited by dry friction forces.Proc. Workshop on Rolling Noise Generation, Berlin (ed.) M Hedel

  • Stelter P, Sextro W 1991 Bifurcations in dynamics systems with dry friction.Int. Ser. Numer. Math. 97: 343–347

    MathSciNet  Google Scholar 

  • Thompson J M T, Stewart H B 1986Nonlinear dynamics and chaos (Chichester: Wiley)

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Institute of Mechanics, University of Hannover, Appelstraße 11, D-30167, Hannover, Germany

    K Popp, N Hinrichs & M Oestreich

Authors
  1. K Popp
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  2. N Hinrichs
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  3. M Oestreich
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Popp, K., Hinrichs, N. & Oestreich, M. Dynamical behaviour of a friction oscillator with simultaneous self and external excitation. Sadhana 20, 627–654 (1995). https://doi.org/10.1007/BF02823210

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