Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory

Ghayesh, Mergen H., Amabili, Marco and Farokhi, Hamed (2013) Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. International Journal of Engineering Science, 63. pp. 52-60. ISSN 0020-7225

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Abstract

The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton's principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency-response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.

Item Type:	Article
Uncontrolled Keywords:	Microbeam; Nonlinear dynamics; Strain gradient elasticity; Stability
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Paul Burns
Date Deposited:	31 Aug 2018 09:26
Last Modified:	11 Oct 2019 19:30
URI:	http://nrl.northumbria.ac.uk/id/eprint/35534

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