The nonlinear dynamics of nanomechanical resonators has drawn great interest for applications in sensing, material characterisation, and for uncovering fundamental interactions at the nanoscale. In this thesis, 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 motion at sum-frequencies. For certain combinations of the fundamental tones and at sufficient drive levels, this motion can be detected. By analysing the amplitude of the response, the relevant nonlinear reduced order model parameters can be extracted.
In this thesis we present a theoretical analysis of a general nonlinear reduced order model excited by two-tone excitation, a description of the methodology to estimate nonlinear terms, and an experimental setup to perform these experiments. The methodology is applied on a string resonator with non-ideal supports, to estimate most nonlinear terms in its modal equations of motion for the first two modes. These results are in relatively good agreement with results estimated using backbone curve estimation and numerical simulations for a string.
The reduced order model, resulting from these measurements done with the presented methodology, could be used for validating nonlinear models, by characterizing nonlinearities in resonant systems, and for designing nonlinear mechanical systems with accurately tuned nonlinear properties.