On the dynamics of imperfect shear deformable microplates

Farokhi, Hamed and Ghayesh, Mergen H. (2018) On the dynamics of imperfect shear deformable microplates. International Journal of Engineering Science, 133. pp. 264-283. ISSN 0020-7225

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Official URL: http://dx.doi.org/10.1016/j.ijengsci.2018.04.011

Abstract

This paper investigates the nonlinear forced dynamical behaviour of a geometrically imperfect viscoelastic shear-deformable microplate. The third-order shear deformation plate theory and the Kelvin–Voigt viscoelastic model are utilised in the framework of the modified version of the couple-stress theory to develop a model for the microsystem. The developed model is in the form of partial differential equations (PDEs) and accounts for geometric nonlinearities, damping nonlinearities, micro-scale size effects, and initial imperfection. Five coupled PDEs are derived for the five independent displacements and rotations. These PDEs are truncated to a set of nonlinearly coupled ordinary differential equations via application of a two-dimensional modal decomposition based on the Galerkin technique. The final set of equations consists of quadratic and cubic nonlinear terms for both damping and stiffness. An efficient numerical algorithm based on a continuation scheme is utilised to analyse the nonlinear forced vibration characteristics of such complicated system. The effects imperfection amplitude, damping nonlinearities, and micro-scale size on forced resonant vibration response are highlighted.

Item Type: Article
Uncontrolled Keywords: Initial imperfection; Third-order shear deformation; Kelvin–Voigt viscoelastic model; Nonlinear resonance; Nonlinear damping; Forced vibration
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 05 Nov 2018 15:04
Last Modified: 05 Nov 2018 15:04
URI: http://nrl.northumbria.ac.uk/id/eprint/36505

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