Summary
In this paper we demonstrate a methodology for the analysis of local bifurcations with codimension one of nonlinear dynamic systems using a combination of analytical and numerical methods. Special emphasis is devoted towards the analysis of mechanical systems with harmonic excitation. Instead of dealing with periodic solutions of the continuous system we study an equivalent approximation of the corresponding Poincaré map. An iterative scheme is used to compute the bifurcation points. The stability analysis for these critical values is carried out using center manifold theory in order to decouple the system into a stable and a low-dimensional critical subsystem. This approach will be demonstrated for the surge motion of a moored pontoon.
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© 1991 Birkhäuser Verlag Basel
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Kleczka, W., Kreuzer, E., Wilmers, C. (1991). Combined Analytical — Numerical Analysis of Nonlinear Dynamical Systems. In: Seydel, R., Schneider, F.W., Küpper, T., Troger, H. (eds) Bifurcation and Chaos: Analysis, Algorithms, Applications. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 97. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7004-7_24
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DOI: https://doi.org/10.1007/978-3-0348-7004-7_24
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7006-1
Online ISBN: 978-3-0348-7004-7
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