Abstract
Impact oscillators arise whenever the components of an oscillator collide with each other or with rigid obstacles. Broadly speaking an impact oscillator combines the behaviour of systems which have smooth dynamics between collisions (or impacts)with discontinuous changes in the dynamics at each impact. Such systems arise frequently in applications both in engineering and in physics and their behaviour can be remarkably rich. They are important, not only because they simulate many real phenomena but also because they introduce much new mathematics and lead naturally to the study of discontinuous dynamical systems. The purpose of these notes is to give an introduction both to the rich variety of the dynamical behaviour of these systems and also to the new mathematical techniques involved in their study.
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
Budd, C. Cliffe K.A. and Dux, F., The effect of frequency and clearence variations on one-dimensional impact oscillators, Bristol University Report AM-93–02, 1993.
Foale, S. and Bishop, S. Dynamical complexities of forced impacting systems, Phil. Trans. R. S.c. Lond., 338, 1992, 547.
Goyda, H. A study of the impact dynamics of loosely supported heat exchanger tubes, Journal of Pressure Vessel Technology, 111, 1989, 394.
Guckenheimer J. and Holmes, P. Nonlinear oscillations, dynamical systems and bifurcations of vector fields Applied Math. Sciences 42,1986, Springer.
Guerts, B., Wiegel, F. and Creswick, R. Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier, Physica, 165A, 1990, 72.
Hogan, S.J. On the dynamics of rigid block motion with harmonic forcing Proc. Roy. S.c. Lond., 425A, 1989, 441.
Katok A. and Strelcyn, J.-M. Invariant manifolds, entropy and billiards; smooth maps with singularities Lecture notes in mathematics, 1222, Springer, 1986.
Lamba, H. and Budd, C. Chaotic, regular and unbounded behaviour in the elastic impact oscillator, Preprint, 1993.
Lehtihet, H. and Miller, B. Numerical study of a billiard in a gravitational field, Physica, 21D, 1993, 986.
Lichtenberg, A. and Lieberman, M. Regular and stochastic motion, Applied Mathematical Sciences, 38, Springer, 1983.
Moon, F. Chaotic vibrations Wiley, 1987.
Nordmark, A. Non-periodic motion caused by grazing incidence in an impact oscillator Journal of Sound and Vibration, 145, 1991, 279.
Pustylnikov, L. On the Fermi-Ulam model Soy. Math. Doklady, 35, 1987, 88.
Shaw, S. a Forced vibrations of a beam with a one sided amplitude constraint Journal of sound and vibration, 99 1985, 459.
Shaw, S. b The dynamics of a harmonically excited system having rigid amplitude constraints, ASME Journal Appl. Mech., 52, 1985, 453.
Shaw, S. and Holmes, P. A periodically forced piecewise linear oscillator, Journal of Sound and Vibration, 90, 1983, 129.
Thompson, J. and Stewart, H. Nonlinear dynamics and chaos, Wiley, 1986.
Ulam S. In Proc. 4th. Berkeley Symp. on Math. Stat. and Prob. 1961.
Whiston, G. a Global dynamics of a vibro-impacting oscillator, Journal of Sound and Vibration, 118, 1987, 395.
Whiston, G. b Singularities in vibro-impact dynamics, Journal of Sound and Vibration, 152, 1992, 427.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Budd, C. (1995). The Global Dynamics of Impact Oscillators. In: Branner, B., Hjorth, P. (eds) Real and Complex Dynamical Systems. NATO ASI Series, vol 464. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8439-5_2
Download citation
DOI: https://doi.org/10.1007/978-94-015-8439-5_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4565-2
Online ISBN: 978-94-015-8439-5
eBook Packages: Springer Book Archive