Abstract
We consider a straight slender visco-elastic beam under periodic axial exci- tation. In order to determine the stability boundary of the undeformed configuration and the parameter domain for periodic solutions we apply different analytical and numerical methods, like simulation of a FE-model and path-following packages for different versions of reduced order models.
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References
Thomsen JJ (2021) Vibrations and Stability - Advanced Theory, Analysis, and Tools. Springer
Thompson JMT, Rainey RCT, Soliman MS, Thompson JMT, Gray P (1990) Ship stability criteria based on chaotic transients from incursive fractals. Philo-sophical Transactions of the Royal Society of London Series A: Physical and Engineering Sciences 332(1624):149–167
Rand RH (2012) Lecture notes on nonlinear vibrations, (online)
Kovacic I, Rand R, Sah SM (2018) Mathieu’s equation and its generalizations: Overview of stability charts and their features. Applied Mechanics Reviews 70(2), 020802
Lacarbonara W (2013) Nonlinear Structural Mechanics - Theory, Dynamical Phenomena and Modeling. Springer
Vetyukov Y (2012) Hybrid asymptotic-direct approach to the problem of finite vibrations of a curved layered strip. Acta Mechanica 223(2):371–385
Wolfram Research, Inc (2022) Mathematica, Version 13.1. Champaign, IL, 2022
Oberle HJ, Grimm W, Berger E (1985) BNDSCO, RechenprogrammzurLösung beschränkter optimaler Steuerungsprobleme. Benutzeranleitung M 8509, Techn. Univ. München
Hairer E, Wanner G (1996) Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics, Springer, Berlin, Heidelberg
Seydel R (1984) A continuation algorithm with step control. In: Numerical methods for bifurcation problems. ISNM 70, Birkhäuser
Bolotin WW (1961) Kinetische Stabilität elastischer Systeme. Mathematik für Naturwissenschaft und Technik, Band 2, VEB Deutscher Verlag der Wissenschaften, Berlin
Dhooge A, Govaerts W, Kuznetsov YA, Meijer HGE, Sautois B (2008) New features of the software MatCont for bifurcation analysis of dynamical systems. MCMDS 14(2):147–175
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Steindl, A., Buchta, R., Ruttmann, M., Vetyukov, Y. (2023). Numerical Investigations of Large Amplitude Oscillations of Planar Parametrically Excited Beams. In: Altenbach, H., Irschik, H., Porubov, A.V. (eds) Progress in Continuum Mechanics. Advanced Structured Materials, vol 196. Springer, Cham. https://doi.org/10.1007/978-3-031-43736-6_24
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DOI: https://doi.org/10.1007/978-3-031-43736-6_24
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