Nonlinear size-dependent dynamics of an imperfect shear deformable microplate

Hamed Farokhi, Mergen H. Ghayesh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)226-242
Number of pages17
JournalJournal of Sound and Vibration
Volume361
Early online date23 Oct 2015
DOIs
Publication statusPublished - 20 Jan 2016

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