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Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system

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Abstract

Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking into account the thermal effects, the nonlinear equations of motion and internal/external boundary conditions are derived through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations with coupling terms. These are solved using the direct multiple-scale method, leading to closed-form solutions for the mode functions, nonlinear natural frequencies and frequency–response curves of the system. The influence of system parameters on the linear and nonlinear natural frequencies, mode functions, and frequency–response curves is studied through numerical parametric analysis. It is shown that the vibration characteristics depend on the mid-plane stretching, intra-span spring, point mass, and temperature change.

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Authors and Affiliations

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

    Mergen H. Ghayesh, Siavash Kazemirad & Pamela Woo

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

    Mohammad A. Darabi

Authors
  1. Mergen H. Ghayesh
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  2. Siavash Kazemirad
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  3. Mohammad A. Darabi
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  4. Pamela Woo
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Correspondence to Mergen H. Ghayesh.

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Ghayesh, M.H., Kazemirad, S., Darabi, M.A. et al. Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system. Arch Appl Mech 82, 317–331 (2012). https://doi.org/10.1007/s00419-011-0558-4

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  • DOI: https://doi.org/10.1007/s00419-011-0558-4

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