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An analytical solution for nonlinear dynamics of a viscoelastic beam-heavy mass system

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Abstract

The aim of this study is to develop an approximate analytic solution for nonlinear dynamic response of a simply-supported Kelvin-Voigt viscoelastic beam with an attached heavy intra-span mass. A geometric nonlinearity due to midplane stretching is considered and Newton’s second law of motion along with Kelvin-Voigt rheological model, which is a two-parameter energy dissipation model, are employed to derive the nonlinear equations of motion. The method of multiple timescales is applied directly to the governing equations of motion, and nonlinear natural frequencies and vibration responses of the system are obtained analytically. Regarding the resonance case, the limit-cycle of the response is formulated analytically. A parametric study is conducted in order to highlight the influences of the system parameters. The main objective is to examine how the vibration response of a plain (i.e. without additional adornment) beam is modified by the presence of a heavy mass, attached somewhere along the beam length.

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, H3A 2K6, Canada

    Mergen H. Ghayesh

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave., Tehran, Iran

    Farbod Alijani

  3. Department of Mechanical Engineering, University of Guilan, Rasht, P.O. Box 1841, Iran

    Mohammad A. Darabi

Authors
  1. Mergen H. Ghayesh
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  2. Farbod Alijani
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  3. Mohammad A. Darabi
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Corresponding author

Correspondence to Mergen H. Ghayesh.

Additional information

This paper was recommended for publication in revised form by Associate Editor Ohseop Song

Mergen H. Ghayesh received his BSc and MSc degrees in Mechanical Engineering from the Mechanical Engineering Department of Iran University of Science and Technology and Tarbiat Modarres University in 2003 and 2007, respectively. In September 2008, he started his PhD program in Mechanical Engineering at McGill University, Canada. His research interests include fluid-structure interactions, nonlinear vibrations and stability, dynamics of nanotubes, perturbation techniques, and dynamics of MEMS.

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Ghayesh, M.H., Alijani, F. & Darabi, M.A. An analytical solution for nonlinear dynamics of a viscoelastic beam-heavy mass system. J Mech Sci Technol 25, 1915–1923 (2011). https://doi.org/10.1007/s12206-011-0519-4

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  • DOI: https://doi.org/10.1007/s12206-011-0519-4

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