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Coupled nonlinear size-dependent behaviour of microbeams

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Abstract

The nonlinear resonant behaviour of a microbeam, subject to a distributed harmonic excitation force, is investigated numerically taking into account the longitudinal as well as the transverse displacement. Hamilton’s principle is employed to derive the coupled longitudinal-transverse nonlinear partial differential equations of motion based on the modified couple stress theory. The discretized form of the equations of motion is obtained by applying the Galerkin technique. The pseudo-arclength continuation technique is then employed to solve the discretized equations of motion numerically. Different types of bifurcations as well as the stability of solution branches are determined. The numerical results are presented in the form of frequency-response and force-response curves for different sets of parameters. The effect of taking into account the longitudinal displacement is highlighted.

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Authors and Affiliations

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

    Mergen H. Ghayesh, Hamed Farokhi & Marco Amabili

Authors
  1. Mergen H. Ghayesh
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  2. Hamed Farokhi
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  3. Marco Amabili
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Correspondence to Mergen H. Ghayesh.

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Ghayesh, M.H., Farokhi, H. & Amabili, M. Coupled nonlinear size-dependent behaviour of microbeams. Appl. Phys. A 112, 329–338 (2013). https://doi.org/10.1007/s00339-013-7787-z

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  • DOI: https://doi.org/10.1007/s00339-013-7787-z

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