Abstract
The free vibration problem is of considerable interest to engineers. When the deflections of the structure are small, a wide range of linear analysis tools can be used and some analytical results are possible. As the deflections become larger, however, geometric nonlinearities are introduced, which result in effects that are not observed in linear systems. Also, when separation or contact of two parts of a system is involved, the characteristic (force-deflect ion) of the system becomes nonlinear. In these situations numerical solution methods must be used with the finite element (FE) approach being the most common (see [1] and [2]).
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References
I. Fried, Nonlinear finite element computation of the equilibrium, stability and motion of the extensional beam and ring, Comput. Methods Appl. Mech. Engrg. 38 (1983), 29–44.
A. Cardona and M. Geradin, A beam finite element nonlinear beam theory with finite rotations, Internat. J. Numer. Methods Engrg. 26 (1988), 2403–2438.
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Fotouhi, R. (2002). Nonlinear Dynamic Analysis of a Curved Beam Structure Using a Finite Element Method. In: Constanda, C., Schiavone, P., Mioduchowski, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0111-3_13
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DOI: https://doi.org/10.1007/978-1-4612-0111-3_13
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6617-4
Online ISBN: 978-1-4612-0111-3
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