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Thermo-mechanical nonlinear dynamics of a buckled axially moving beam

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Abstract

The thermo-mechanical nonlinear dynamics of a buckled axially moving beam is numerically investigated, with special consideration to the case with a three-to-one internal resonance between the first two modes. The equation of motion of the system traveling at a constant axial speed is obtained using Hamilton’s principle. A closed form solution is developed for the post-buckling configuration for the system with an axial speed beyond the first instability. The equation of motion over the buckled state is obtained for the forced system. The equation is reduced into a set of nonlinear ordinary differential equations via the Galerkin method. This set is solved using the pseudo-arclength continuation technique to examine the frequency response curves and direct-time integration to construct bifurcation diagrams of Poincaré maps. The vibration characteristics of the system at points of interest in the parameter space are presented in the form of time histories, phase-plane portraits, and Poincaré sections.

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Authors and Affiliations

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

    Siavash Kazemirad, Mergen H. Ghayesh & Marco Amabili

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  1. Siavash Kazemirad
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  2. Mergen H. Ghayesh
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  3. Marco Amabili
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Correspondence to Mergen H. Ghayesh.

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Kazemirad, S., Ghayesh, M.H. & Amabili, M. Thermo-mechanical nonlinear dynamics of a buckled axially moving beam. Arch Appl Mech 83, 25–42 (2013). https://doi.org/10.1007/s00419-012-0630-8

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  • DOI: https://doi.org/10.1007/s00419-012-0630-8

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