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

Planar driven nanowire oscillators are susceptible to undergo whirling motion due to coupling between flexural planar and nonplanar modes of vibration. This investigation is concerned with planar to whirling motion transition in the oscillation of an electrostatically actuated nanowire, which is pre-deflected due to applied DC voltage. We have derived dynamical equations of motion using Euler-Bernoulli beam theory and Galerkin formulation as reduced order model of the governing coupled partial differential equations. The dynamical equations have been solved using second-order averaging method and the averaging solution has been validated by comparing with the numerical solution of the reduced order model. Further, planar to whirling motion transition has been investigated by studying qualitative changes in resonance curves with variation of electrostatic actuation. In this paper, we provide a simple analytical condition which takes into account the effects of DC voltage for prediction of initiation of whirling motion. Our main observation of the present investigation is that DC voltage can tune the initiation pattern of the whirling motion and change the qualitative nature of resonance curves.