Nanomechanical resonators show higher order nonlinearity at room temperature

Abstract

Most mechanical resonators are treated as simple linear oscillators. Nonlinearity in the resonance behavior of nanoelectromechanical systems (NEMS) has only lately attracted significant interest. Most recently, cubic-order nonlinearity has been used to explain anomalies in the resonance frequency behaviors in the frequency domain. Particularly, such nonlinearities were explained using cubic nonlinearity in the restoring force (Duffing nonlinearity) or damping (van der Pol nonlinearity). Understanding the limits of linear resonant behavior is particularly important in NEMS, as they are frequently studied for their potential in ultrasensitive sensing and detection, applications that most commonly assume a linear behavior to transduce motion into a detected signal. In this paper, we report that even at low excitation, cubic nonlinearity is insufficient to explain nonlinearity in graphene NEMS. Rather, we observe that higher order, in particular, the fifth order effects need to be considered even for systems at room temperature with modest quality factors. These are particularly important results that could determine the limits of linear detection in such systems and quite possibly present unconventional avenues for ultrasensitive detection paradigms using nonlinear dynamics. Such intriguing possibilities, however, hinge crucially on a superior understanding and exploitation of these inherent nonlinearities as opposed to modeling them as approximated linear or cubic systems.