Summary
The nonlinear dynamics of nanomechanical resonators has drawn great interest for applications in sensing, material characterisation and for uncovering fundamental interactions at the nanoscale. Here, we explore multi-tone excitation as a route towards extracting the full nonlinear reduced order model of a multi-mode nanomechanical resonator. By driving at two frequencies, the nonlinear terms in the equation of motion will cause the generation of sum and difference frequencies. When these combination frequencies align with a natural resonance frequency of the resonator, they can be detected. We present an experimental methodology to perform these experiments and show how we can extract the relevant nonlinear reduced order model parameters by analyzing the amplitude of the response. The resulting experimentally extracted reduced order model can be used for validating nonlinear models, for characterizing nonlinearities in resonant systems, for estimating the magnitude of physics induced nonlinearities and for designing nonlinear mechanical systems with accurately tuned nonlinear properties. In this work we present the methodology and initial experimental results.
