Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators

A M Eriksson, D Midtvedt, A Croy, A Isacsson
2013 Nanotechnology  
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
more » ... ith 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.
doi:10.1088/0957-4484/24/39/395702 pmid:24008430 fatcat:wlekny4sw5amzcl3ywztur2g7a