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Modal interactions in primary and subharmonic resonant dynamics of imperfect microplates with geometric nonlinearities

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Abstract

This paper analyses the modal interactions in the nonlinear, size-dependent dynamics of geometrically imperfect microplates. Based on the modified couple stress theory, the equations of motion for the in-plane and out-of-plane motions are obtained employing the von Kármán plate theory as well as Kirchhoff’s hypotheses by means of the Lagrange equations. The equations of motions are solved using the pseudo-arclength continuation technique and direct time-integration method. The system parameters are tuned to the values associated with modal interactions, and then nonlinear resonant responses and energy transfer are analysed. Nonlinear motion characteristics are shown in the form of frequency-response and force-response curves, time histories, phase-plane portraits, and fast Fourier transforms.

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montreal, QC, H3A 0C3, Canada

    Hamed Farokhi

  2. School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, Wollongong, 2522, NSW, Australia

    Mergen H. Ghayesh

Authors
  1. Hamed Farokhi
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  2. Mergen H. Ghayesh
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Correspondence to Mergen H. Ghayesh.

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Farokhi, H., Ghayesh, M.H. Modal interactions in primary and subharmonic resonant dynamics of imperfect microplates with geometric nonlinearities. Acta Mech. Sin. 32, 469–480 (2016). https://doi.org/10.1007/s10409-015-0536-0

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  • DOI: https://doi.org/10.1007/s10409-015-0536-0

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