A size-dependent nonlinear third-order shear-deformable dynamic model for a microplate on an elastic medium

Ghayesh, Mergen H., Farokhi, Hamed, Hussain, Shahid, Gholipour, Alireza and Arjomandi, Maziar (2017) A size-dependent nonlinear third-order shear-deformable dynamic model for a microplate on an elastic medium. Microsystem Technologies, 23 (8). pp. 3281-3299. ISSN 0946-7076

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Official URL: http://dx.doi.org/10.1007/s00542-016-3096-8

Abstract

This paper develops a size-dependent nonlinear third-order shear-deformable model for the dynamic analysis of microplates. Taking into account in-plane and out-of-plane displacements and inertia as well as rotations (via using the third-order shear deformation theory) and the modified couple stress theory, the Lagrange equations are employed to derive the equations of motion. An assumed-mode technique is applied to the expressions for the elastic strain energy of the microplate, the elastic potential energy due to the translational springs, the kinetic energy of the microplate, the energy dissipation function due to damping, and the work of a harmonically varying external loading on the microplate; these expressions are then inserted in the Lagrange equations in order to obtain the discretised equations of motion as nonlinear coupled functions of generalized coordinates. The pseudo-arclength continuation technique and a direct time-integration are employed to solve these equations and to obtain the generalized coordinates, hence system responses, numerically. Apart from the nonlinear analysis, a linear analysis is conducted by means of an eigenvalue analysis. The motion behaviour of the system is analysed and the importance of employing the modified couple stress theory, rather than the classical continuum theory, is discussed.

Item Type: Article
Uncontrolled Keywords: Elastic Foundation, Modify Couple Stress Theory, Modify Couple Stress, Strain Gradient Elasticity Theory, Classical Continuum Theory
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Paul Burns
Date Deposited: 14 Aug 2018 11:54
Last Modified: 14 Aug 2018 11:54
URI: http://nrl.northumbria.ac.uk/id/eprint/35328

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