Related Experiment Video
Updated: May 8, 2026

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
Published on: February 4, 2018
Frequency tuning, nonlinearities and mode coupling in circular mechanical graphene resonators
A M Eriksson1, D Midtvedt, A Croy
1Department of Applied Physics, Chalmers University of Technology SE-412 96, Göteborg, Sweden.
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 the geometrical nonlinearity the mode dynamics can be modeled by coupled Duffing equations. By solving the Airy stress problem we obtain analytic expressions for the eigenfrequencies and nonlinear coefficients as functions of the 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.
Related Concept Videos
Sound Waves: Resonance
Design Example: Underdamped Parallel RLC Circuit
Starting with a fixed...
Modes of Standing Waves - I
Parallel Resonance
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.
Standing Waves in a Cavity

