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Planar driven nanowire oscillators are susceptible to undergo whirling motiondue to coupling between flexural planar and nonplanar modes of vibration. Thisinvestigation is concerned with planar to whirling motion transition in theoscillation of an electrostatically actuated nanowire, which is pre-deflecteddue to applied DC voltage. We have derived dynamical equations of motion usingEuler-Bernoulli beam theory and Galerkin formulation as reduced order model ofthe governing coupled partial differential equations. The dynamical equationshave been solved using second-order averaging method and the averaging solutionhas been validated by comparing with the numerical solution of the reducedorder model. Further, planar to whirling motion transition has beeninvestigated by studying qualitative changes in resonance curves with variationof electrostatic actuation. In this paper, we provide a simple analyticalcondition which takes into account the effects of DC voltage for prediction ofinitiation of whirling motion. Our main observation of the presentinvestigation is that DC voltage can tune the initiation pattern of thewhirling motion and change the qualitative nature of resonance curves.

Effects of DC voltage on initiation of whirling motion of an electrostatically actuated nanowire oscillator