Size-dependent large-amplitude oscillations of microcantilevers

Ghayesh, Mergen H. and Farokhi, Hamed (2017) Size-dependent large-amplitude oscillations of microcantilevers. Microsystem Technologies, 23 (8). pp. 3477-3488. ISSN 0946-7076

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Abstract

The size-dependent oscillations of a microcantilever with a tip (end) mass and a spring support undergoing a large-amplitude motion is analysed theoretically, taking into account curvature-related nonlinearities. Modelling small-size effects via use of the modified couple stress theory, the size-dependent potential and kinetic energies of the system are obtained. The continuous models for the motion behaviour of the microcantilever are developed via use of an energy method on the basis of Hamilton’s principle. Application of the centreline-inextensibility in oscillation course of the microcantilever results in a continuous model of the system with nonlinear inertial terms, which when coupled with curvature nonlinearities produces a highly nonlinear system. A weighted-residual method is then employed to truncate the continuous model, yielding the reduced-order model of the microcantilever motion with a generalised-coordinate-dependent mass matrix (due to inertial nonlinearities); a coupled continuation-time-integration method is then employed for the numerical simulations. The large-amplitude oscillation behaviour of the system is examined by constructing the frequency–responses and force-responses. The effect of the size of the end-mass on the nonlinear oscillation behaviour of the microcantilever is analysed. The importance of taking into account different nonlinearity sources is discussed. It is shown that the modified couple stress theory results in a stronger softening behaviour when compared to the classical continuum mechanics.

Item Type:	Article
Uncontrolled Keywords:	Modify Couple Stress Theory, Resonant Region, Timoshenko Microbeam, Symmetric Curvature Tensor, Small Excitation Frequency
Subjects:	H300 Mechanical Engineering
Department:	Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User:	Paul Burns
Date Deposited:	22 Aug 2018 13:04
Last Modified:	11 Oct 2019 19:30
URI:	http://nrl.northumbria.ac.uk/id/eprint/35439

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