Nonlinear Modal Interactions and Internal Resonance in a Micromachined Disk Resonator

In this paper, nonlinear modal interactions in a micromachined disk resonator with 2:1 internal resonance are demonstrated. By means of the multiple scales method, two types of transition from stable to unstable behavior including jump phenomena and modulated motion corresponding to M-shaped responses are explained in a coupled nonlinear system dominated by quadratic nonlinearity. At the same time, these exotic responses and stability under different driving forces and the strength of internal resonance are also investigated. Furthermore, the frequency and amplitude stability and signal-to-noise ratio (SNR) can be improved under this condition.