Bifurcation diagram and dynamic response of a MEMS resonator with a 1:3 internal resonance

The dynamic response of a nonlinear resonator in the presence of resonant mode coupling is studied experimentally and theoretically. For the case of a clamped-clamped beam resonator in the presence of a 1:3 internal resonance, we show that at the onset of internal resonance, steady state oscillations cannot be sustained. At higher drive levels, stable oscillations can be maintained but the resonator amplitude undergoes amplitude modulated responses. We use these dynamic responses to build a bifurcation diagram that can be described remarkably well with a simple model consisting of a Duffing resonator coupled to a linear one.