Abstract
In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.
Highlights
The history of parametric oscillations dates back to the 19th century and the observation of surface waves in the famous singing wineglass experiment of Michael Faraday[1]
It is well known that above a certain critical force of this parametric pump, the device will become unstable and exhibit parametric resonance[2,31,32]. Such behavior has been previously observed, the nonlinear dynamics involved in parametric resonance has received less attention
We demonstrate that parametric resonance holds important information about the nonlinear damping of graphene that has been a subject of strong debate in the community[28,33,34,35,36]
Summary
The history of parametric oscillations dates back to the 19th century and the observation of surface waves in the famous singing wineglass experiment of Michael Faraday[1]. It is well known that above a certain critical force of this parametric pump, the device will become unstable and exhibit parametric resonance[2,31,32] Such behavior has been previously observed, the nonlinear dynamics involved in parametric resonance has received less attention. Excited nonlinear mechanical response is analyzed and a model is proposed that can simulate both parametric and directly driven responses This nonlinear Duffing response, caused by the direct drive, has previously been studied to obtain the stiffness properties of graphene devices[37,38]. Period doubling bifurcations are almost fully governed by the linear dissipation terms, while the saddle node bifurcation of the parametric resonance is fully governed by nonlinear dissipation terms[32] From this analysis, we can conclude that nonlinear damping in graphene can be accurately described by a dissipation term of the van der Pol type. This unexpected deviation from the theoretical response suggests that unconventional dynamic phenomena are governing the linewidth of graphene resonators
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