Frequency tuning, nonlinearities and mode coupling in circular graphene resonators

Abstract

We study circular nanomechanical graphene resonators by means of continuum elasticity theory, treating them as membranes. We derive dynamic equations for the flexural mode amplitudes. Due to geometrical nonlinearity these can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for eigenfrequencies and nonlinear coefficients as functions of radius, suspension height, initial tension, back-gate voltage and elastic constants, which we compare with finite element simulations. Using perturbation theory, we show that it is necessary to include the effects of the non-uniform stress distribution for finite deflections. This correctly reproduces the spectrum and frequency tuning of the resonator, including frequency crossings.

21 pages, 7 figures, 3 tables

References in corpus (26)

• Intrinsic ripples in graphene
• Ripple Texturing of Suspended Graphene Atomic Membranes
• Performance of Monolayer Graphene Nanomechanical Resonators with Electrical Readout
• Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes
• Imaging mechanical vibrations in suspended graphene sheets
• Coherent phonon manipulation in coupled mechanical resonators
• Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes
• Nonlinear modal interactions in clamped-clamped mechanical resonators
• Nonlinear Dynamics and Chaos in Two Coupled Nanomechanical Resonators
• Continuum elastic modeling of graphene resonators
• Coherent control of a nanomechanical two-level system
• Stamp transferred suspended graphene mechanical resonators for radio-frequency electrical readout
• Electrostatic Graphene Loudspeaker
• Radio frequency electrical transduction of graphene mechanical resonators
• Strong coupling between mechanical modes in a nanotube resonator
• Suppression of anharmonicities in crystalline membranes by external strain
• Graphene as a Prototype Crystalline Membrane
• Nonlinear Damping in Graphene Resonators
• The Importance of Edge Effects on the Intrinsic Loss Mechanisms of Graphene Nanoresonators
• Frequency tuning, nonlinearities and mode coupling in circular graphene resonators
• Narrowband nanomechanical mass measurement using nonlinear response of a graphene membrane
• High-Q optomechanical GaAs nanomembranes
• Strongly coupled modes in a weakly driven micromechanical resonator
• Coupling between quantum Hall state and electromechanics in suspended graphene resonator
• Mechanical cat states in graphene resonators
• Multi-phonon relaxation and generation of quantum states in a nonlinear mechanical oscillator

Cited by in corpus (24)

• Coupling graphene mechanical resonators to superconducting microwave cavities
• Dynamical strong coupling and parametric amplification in mechanical modes of graphene drums
• Young's modulus of 2D materials extracted from their nonlinear dynamic response
• Dissipative optomechanical preparation of macroscopic quantum superposition states
• Frequency tuning, nonlinearities and mode coupling in circular graphene resonators
• Symmetry-breaking induced frequency combs in graphene resonators
• FPU physics with nanomechanical graphene resonators: intrinsic relaxation and thermalization from flexural mode coupling
• Time-domain response of atomically thin $\mathrm{Mo}{\mathrm{S}}_2$ nanomechanical resonators
• Coherent phonon Rabi oscillations with a high frequency carbon nanotube phonon cavity
• Entangled-state generation and Bell inequality violations in nanomechanical resonators
• Strain-dependent damping in nanomechanical resonators from thin $\mathrm{Mo}{\mathrm{S}}_2$ crystals
• Simultaneous Electrical and Optical Readout of Graphene-Coated High Q Silicon Nitride Resonators
• Snap-through transition of graphene membranes for memcapacitor applications: A combined study using MD, DFT and elasticity theory
• Scattering of flexural acoustic phonons at grain boundaries in graphene
• Graphene nanodrums as valleytronic devices
• Sound waves induce Volkov-like states, band structure and collimation effect in graphene
• Valence force model and nanomechanics of single-layer phosphorene
• Particle number scaling for diffusion-induced dissipation in graphene and carbon nanotube nanomechanical resonators
• Tension mediated nonlinear coupling between orthogonal mechanical modes of nanowire resonators
• Eigenmodes and resonance vibrations of 2D nanomembranes -- Graphene and hexagonal boron-nitride
• Thermal expansion in nanoresonators
• Nanomechanical resonators show higher order nonlinearity at room temperature
• Switching off energy decay channels in nanomechanical resonators
• Stepwise relaxation and stochastic precession in degenerate oscillators dispersively coupled to particles