Tuning nonlinear damping in graphene nanoresonators by parametric\u2013direct internal resonance

Ata Keşkekler,Herre S J Van Der Zant,Oriel Shoshani,Martin Lee,Farbod Alijani,Peter G Steeneken

doi:10.1038/s41467-021-21334-w

Ata Keşkekler, Herre S J Van Der Zant + Show 4 more

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https://doi.org/10.1038/s41467-021-21334-w

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Abstract

Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range.

Highlights

Mechanical sources of nonlinear damping play a central role in modern physics, from solidstate physics to thermodynamics
We demonstrate that nonlinear damping of graphene nanodrums can be strongly enhanced by parametric–direct internal resonance (IR), providing supporting evidence for the microscopic theory of nonlinear dissipation[10,32]
We bring the fundamental mode of the nanodrum into parametric resonance at twice its resonance frequency, allowing it to be tuned over a wide frequency range from 40 to 70 MHz

Summary

Introduction

Mechanical sources of nonlinear damping play a central role in modern physics, from solidstate physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. Amongst the different mechanisms that affect nonlinear damping, intermodal coupling is interesting, as it can be enhanced near internal resonance (IR), a special condition at which the ratio of the resonance frequencies of the coupled modes is a rational number[19]. This phenomenon has frequently been observed in nano/micromechanical resonators[20,21,22,23,24,25,26,27,28,29]. By comparing the characteristic dependence of the nonlinear damping coefficient on parametric drive to a theoretical model, we confirm that IR can be held accountable for the significant increase in nonlinear damping

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