  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.
