Size-dependent parametric dynamics of imperfect microbeams

Farokhi, Hamed and Ghayesh, Mergen H. (2016) Size-dependent parametric dynamics of imperfect microbeams. International Journal of Engineering Science, 99. pp. 39-55. ISSN 0020-7225

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Official URL: http://dx.doi.org/10.1016/j.ijengsci.2015.10.014

Abstract

The nonlinear parametric dynamics of a geometrically imperfect microbeam subject to a time-dependent axial load is investigated in this paper. Based on the Euler-Bernoulli beam theory and the modified couple stress theory, continuous models for kinetic and potential energies are developed and balanced via use of Hamilton's principle. A model reduction procedure is carried out by applying the Galerkin scheme coupled with an assumed-mode technique, yielding a high-dimensional second-order reduced-order model. A linear analysis is performed upon the linear part of the reduced-order model in order to obtain the linear size-dependent natural frequencies. A nonlinear analysis is performed on the reduced-order model using the pseudo-arclength continuation method and a direct time-integration technique, yielding generalised coordinates, and hence the system parametric response. It is shown that, the steady-state frequency-response curves possess a trivial solution, both stable and unstable, throughout the solution space, separated by period-doubling bifurcation points, from which non-trivial solution branches bifurcate.

Item Type: Article
Uncontrolled Keywords: Modified couple stress theory; Imperfect microbeam; Time-dependent axial load; Dynamics
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 24 Aug 2018 10:51
Last Modified: 24 Aug 2018 10:51
URI: http://nrl.northumbria.ac.uk/id/eprint/35475

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