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Nonlinear equations for a thin beam

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Summary

Finite oscillations of a thin beam are analyzed, taking into account large deflections and rotations with small strains. It is shown that, depending on the assumptions, problems for an elastic and viscoelastic beam lead to solving hyperbolic or parabolic nonlinear partial differential equations. As an example, a cantilever beam is considered. The solutions for nonlinear vibrations are obtained by means of the Galerkin method, and numerical results are presented graphically for four material models.

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  1. Institute of Fundamental Technological Research, ul. Świętokrzyska 21 00-049 Warsaw and Kielce University of Technology Faculty of Management and Computer Modelling, Al. 1000-cia Państwa Polskiego 7 Budynek C, 25-314, Kielce, Poland

    A. Pielorz

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  1. A. Pielorz
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Correspondence to A. Pielorz.

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Pielorz, A. Nonlinear equations for a thin beam. Acta Mechanica 167, 1–12 (2004). https://doi.org/10.1007/s00707-003-0058-x

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  • DOI: https://doi.org/10.1007/s00707-003-0058-x

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