On some bifurcation analysis techniques for continuous systems
Banichuk, N., Barsuk, A., Jeronen, J., Neittaanmäki, P., & Tuovinen, T. (2016). On some bifurcation analysis techniques for continuous systems. Rakenteiden mekaniikka, 49(2), 52-68. http://rmseura.tkk.fi/rmlehti/2016/nro2/RakMek_49_2_2016_3.pdf
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© The Authors 2016. This is an open access article distributed under the terms of a CC BY-SA 4.0 license.
This paper is devoted to techniques in bifurcation analysis for continuous mechanical systems, concentrating on polynomial equations and implicitly given functions. These are often encountered in problems of mechanics and especially in stability analysis. Taking a classical approach, we summarize the relevant features of the cubic polynomial equation, and present some new aspects for asymptotics and parametric representation of the solutions. This is followed by a brief look into the implicit function theorem as a tool for analyzing bifurcations. As an example from mechanics, we consider bifurcations in the transverse free vibration problem of an axially compressed beam.
PublisherRakenteiden Mekaniikan Seura ry
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Except where otherwise noted, this item's license is described as © The Authors 2016. This is an open access article distributed under the terms of a CC BY-SA 4.0 license.
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