Nonlinear size-dependent dynamics of an imperfect shear deformable microplate

Farokhi, Hamed and Ghayesh, Mergen H. (2016) Nonlinear size-dependent dynamics of an imperfect shear deformable microplate. Journal of Sound and Vibration, 361. pp. 226-242. ISSN 0022-460X

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Official URL: http://dx.doi.org/10.1016/j.jsv.2015.09.025

Abstract

The nonlinear size-dependent dynamics of a geometrically imperfect shear deformable microplate is investigated based on the modified couple stress theory. An initial imperfection in the out-of-plane direction is taken into account. The third-order shear deformation theory is employed to model the system by retaining in-plane displacements and inertia. The governing equations of motion of the system are obtained employing an energy method through use of the Lagrange equations, which upon employing an assumed-mode technique, yields a set of second-order nonlinear ordinary differential equations with coupled terms. A high-dimensional discretised system is considered and made double-dimensional via a change of variables in order to obtain a set of first-order nonlinear ordinary differential equations. The resulting equations are solved using a direct time-integration technique, resulting in time-dependent generalised coordinates for the in-plane and out-of-plane displacements and two rotations. From these generalised coordinates, phase-plane portraits and fast Fourier transforms (FFTs) are also obtained. Moreover, the frequency-response and force-response curves of the system are obtained using a continuation technique; stability analysis is conducted via the Floquet theory. The effect of the initial imperfection as well as the length-scale parameter on the system response is also examined.

Item Type: Article
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 24 Aug 2018 11:15
Last Modified: 24 Aug 2018 11:15
URI: http://nrl.northumbria.ac.uk/id/eprint/35479

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