Characterizing multi-mode nonlinear dynamics of nanomechanical resonators

TL;DR

This paper introduces a physics-based reduced-order modeling approach for nanomechanical resonators that accurately captures complex nonlinear dynamics across multiple modes and frequency ranges, validated through experiments on graphene nanodrums.

Contribution

A novel FEM-based reduced-order modeling methodology that predicts nonlinear behaviors of nanomechanical resonators without empirical fitting, linking geometry and material properties to dynamic responses.

Findings

Model accurately predicts multi-stability and parametric resonance.

Experimental validation on graphene nanodrum confirms model's effectiveness.

Captures nonlinear phenomena over a 70 MHz frequency span.

Abstract

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modelling methodology based on FEM simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven opto-thermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multi-stability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behaviour.