Abstract
The impact oscillator is one of the simplest mechanical systems with the strong nonlinearity (Fig.l(a)), which is caused by a sudden change of stiffness during the contact of impacting bodies. When the time duration of the impact can be assumed negligibly short, then the Newton elementary theory of impact is used for the investigation of the system dynamics. This problem was investigated from many points of view. The paper introduces a short review of results and concentrates on the explaining the substance of four ways from periodic to chaotic impact motions, especially on the interrupted Feigenbaum cascade and the interrupted development of the saddle-node instability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bespalova, L.V. (1956) On the theory of the vibro-impact system, Izv. AN SSSR, OTN, No..3,3-14 (in Russian).
Irie, T., Yamada, G., Matsuzaki, H. (1974) On the dynamic response of a vibro impact system to random force, Bull, of the Faculty of Eng., Hokkaido University, No.72, 13-24.
Kotera, T., Peterka, F. (1981) Part IV — Analytical solution of the (2/n)-impact motion and its stability, Acta Technica CSAV, No.6, 747-758.
Kotera, T., Peterka, F. (1984) Part VI — Analytical and analogue solution of the multi-impact motion and its stability, Acta Technica CSAV, No.3, 255-279.
Nordmark, A.B. (1991) Non-periodic motion caused by grazing incidence in an impact oscillator, Journal of Sound and Vibration, 145(2), 279–297.
Peterka, F. (1974a) Part I-Theoretical analysis of n-multiple (l/n)-impact motions, Acta Technica CSAV, No.4, 462-473.
Peterka, F. (1974b) Part II-Results of analogue computer modelling of the motion, Acta Technica CSAV, No.5, 569-580.
Peterka, F. (1981) Introduction to vibration of mechanical systems with internal impacts, ACADEMIA Publishing House, Prague, (in Czech).
Peterka, F., Vacik, J. (1981) Part III-Statistical characteristics of beat motions, Acta Technica CSAV, No.2, 161-184.
Peterka, F., Kotera, T. (1982) Part V-Regions of existence and stability and domains of attraction of different kinds of impact motion, Acta Technica CSAV, No.l, 92-117.
Peterka, F., Čipera, S. (1994) Chatic motions in mechanical systems with impacts, In Proc. Chaos and nonlinear mechanics, World Scientific Series on Nonlinear Science, Series B, Vol.4, 265–276.
Peterka, F., Kotera, T. (1996) Four ways from periodic to chaotic motion in the impact oscillator. Machine Vibration, 1996, 5, 71–81.
Peterka, F. (1996) Bifurcations and transition phenomena in an impact oscillator. Chaos, Solitons & Fractals, Vol.7, No. 10, 1635–1647.
Peterka, F., SzöUös, O. (1997) Dynamics of the opposed pile driver, In Proc. IUTAM Symposium “Interaction between Dynamics and Control in Advanced Mechanical Systems”, D.H. van Campen (ed.), Springer Science+Business Media Dordrecht, Solid Mechanics and its Applications, Vol.52, 271-278.
Rusakov, I.G., Kharkevich, A.A. (1942) Excited vibration of the system impacting against the stop, Journal of Technical Physics (ZhTF), Vol.12, No.l 1–12 (in Russian).
Sachse, R., Reum, G. (1965) Beiträge zur Theorie des Kurbel-Feder-Hammers (Teil I)-Der Kurbel-Feder Hammer als Ein-Masse System mit linearer Federkennlinie. Wissenschaftliche Zeitschrift der Technischen Hochschule Karl-Marx-Stadt, Jahrgang VII, Heft 2, 39–53.
Shaw, S.W., Holmes, P.J. (1983) A periodically forced piecewise linear oscillator. J. of Sound and Vibration, 90(1), 129–155.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Peterka, F. (1999). Dynamics of the Impact Oscillator. In: Moon, F.C. (eds) IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics. Solid Mechanics and its Applications, vol 63. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5320-1_29
Download citation
DOI: https://doi.org/10.1007/978-94-011-5320-1_29
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6235-0
Online ISBN: 978-94-011-5320-1
eBook Packages: Springer Book Archive