Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams

Ghayesh, Mergen H. and Farokhi, Hamed (2015) Coupled Nonlinear Dynamics of Geometrically Imperfect Shear Deformable Extensible Microbeams. Journal of Computational and Nonlinear Dynamics, 11 (4). 041001. ISSN 1555-1415

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Official URL: http://dx.doi.org/10.1115/1.4031288

Abstract

This paper aims at analyzing the coupled nonlinear dynamical behavior of geometrically imperfect shear deformable extensible microbeams based on the third-order shear deformation and modified couple stress theories. Using Hamilton's principle and taking into account extensibility, the three nonlinear coupled continuous expressions are obtained for an initially slightly curved (i.e., a geometrically imperfect) microbeam, describing the longitudinal, transverse, and rotational motions. A high-dimensional Galerkin scheme is employed, together with an assumed-mode technique, in order to truncate the continuous system with an infinite number of degrees of freedom into a discretized model with sufficient degrees of freedom. This high-dimensional discretized model is solved by means of the pseudo-arclength continuation technique for the system at the primary resonance, and also by direct time-integration to characterize the dynamic response at a fixed forcing amplitude and frequency; stability analysis is conducted via the Floquet theory. Apart from analyzing the nonlinear resonant response, the linear natural frequencies are obtained via an eigenvalue analysis. Results are shown through frequency-response curves, force-response curves, time traces, phase-plane portraits, and fast Fourier transforms (FFTs). The effect of taking into account the length-scale parameter on the coupled nonlinear dynamic response of the system is also highlighted.

Item Type: Article
Uncontrolled Keywords: Rotation, Stress, Shear (Mechanics), Frequency response, Microbeams, Resonance, Nonlinear dynamics, Bifurcation
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 23 Aug 2018 16:38
Last Modified: 23 Aug 2018 16:38
URI: http://nrl.northumbria.ac.uk/id/eprint/35463

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