Summary
The finite motions of a suspended elastic cable subjected to a planar harmonic excitation is studied through one ordinary equation with quadratic and cubic nonlinearities. The onset of chaotic motions in the neighbourhood of the 1/2 subharmonic resonance condition is analysed via numerical simulations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Benedettini, F. and Rega, G., Nonlinear dynamics of an elastic cable under planar excitation, Int. J. Non-Linear Mech. 22 497–509(1987).
Takahashi, K. and Konishi, Y., Non-linear vibrations of cables in three dimensions, Part II: Out-of-plane vibrations under in-plane sinusoidally time-varying load, J. Sound Vibrat. 118, 85–97 (1987).
Rega, G. and Benedettini, F., Planar nonlinear oscillations of elastic cables under subharmonic resonance conditions, J. Sound Vibrat. (to appear) (1989)
Szemplinska-Stupnicka, W. and Bajkowski, J., The 1/2 subharmonic resonance and its transition to chaotic motion in a non-linear oscillator, Int. J. Non-linear Mech. 21, 401–419 (1986).
Thompson, J.M.T. and Stewart, H.B., Nonlinear dynamics and chaos. Wiley, Chichester (1986).
Moon, F., Chaotic vibrations. Wiley, New York (1987)
Tongue, B.H., Characteristics of numerical simulations of chaotic systems, ASME J. Appt. Mech. 54, 695–699 (1987).
Kreuzer, E.J., On the numerical study of bifurcation problems, in Bifurcations: Analysis, algorithms, applications (Eds. T. Küpper, R.Seydel and H. Troger ), 161–171, Birkhäuser, Basel (1987).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Benedettini, F., Rega, G. (1990). 1/2 Subharmonic Resonance and Chaotic Motions in a Model of Elastic Cable. In: Schiehlen, W. (eds) Nonlinear Dynamics in Engineering Systems. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83578-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-83578-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83580-3
Online ISBN: 978-3-642-83578-0
eBook Packages: Springer Book Archive