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Vibrations of Beams in the Elasto-Plastic and Geometrically Nonlinear Regime

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Exploiting Nonlinear Behavior in Structural Dynamics

Part of the book series: CISM Courses and Lectures ((CISM,volume 536))

Abstract

This chapter presents models for beams vibrating with moderately large displacements and with elasto-plasticity. The beams are initially straight, homogeneous and isotropic, and oscillate always in one plane. A method to solve the equations of motion in the time domain, with computation of plastic strains in a mixed hardening situation, is described. Forced oscillations under harmonic excitations are analysed using this method. A frequency domain procedure to analyse free vibrations with existing plastic strains is also introduced. Free vibration oscillations are then analysed, with particular attention to the combined influence of large displacements, i.e., geometrical nonlinearity, and plastic strains on the shapes assumed during the period of vibration and on the natural frequencies.

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  1. DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

    Pedro Ribeiro

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  1. Pedro Ribeiro
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  1. University of Bristol, Great Britain

    David J. Wagg

  2. Duke University, Duham, NC, USA

    Lawrence Virgin

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Ribeiro, P. (2012). Vibrations of Beams in the Elasto-Plastic and Geometrically Nonlinear Regime. In: Wagg, D.J., Virgin, L. (eds) Exploiting Nonlinear Behavior in Structural Dynamics. CISM Courses and Lectures, vol 536. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1187-1_5

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