Coupled longitudinal-transverse-rotational behaviour of shear deformable microbeams

Ghayesh, Mergen H. and Farokhi, Hamed (2015) Coupled longitudinal-transverse-rotational behaviour of shear deformable microbeams. Composites Part B: Engineering, 77. pp. 319-328. ISSN 1359-8368

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Official URL: http://dx.doi.org/10.1016/j.compositesb.2015.03.03...

Abstract

In this paper, for the first time, the nonlinear motion characteristics of a hinged-hinged third-order shear deformable microbeam are examined, based on the modified couple stress theory and the third-order shear deformation theory. The extensibility of the microbeam is modelled by taking into account the longitudinal displacement. The nonlinear equations governing the longitudinal, transverse, and rotational motions are derived by means of Hamilton's principle in conjunction with the modified couple stress theory (to take into account small-scale effects). The three coupled nonlinear partial differential equations are discretized via the Galerkin method and the resulting set of ordinary differential equations is solved by means of the pseudo-arclength continuation technique and via direct time-integration. The effects of the system parameters on the behaviour of the microbeam are studied. Results are presented in the form of frequency-responses and force-responses. Points of interest in the parameter space are also highlighted in the form of time histories, phase-plane portraits, and fast Fourier transforms (FFTs). Moreover, the similarities and differences in the response of the system obtained via the modified couple stress and classical continuum mechanics theories are discussed.

Item Type: Article
Uncontrolled Keywords: Resins; Microstructures; Micro-mechanics; Numerical analysis
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 24 Aug 2018 12:02
Last Modified: 24 Aug 2018 12:02
URI: http://nrl.northumbria.ac.uk/id/eprint/35484

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