Size-dependent large-amplitude oscillations of microcantilevers

Mergen H. Ghayesh*, Hamed Farokhi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)3477-3488
Number of pages12
JournalMicrosystem Technologies
Issue number8
Early online date30 Nov 2016
Publication statusPublished - 1 Aug 2017


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