Dispersive and Dissipative Coupling in a Micromechanical Resonator Embedded with a Nanomechanical Resonator

A micromechanical resonator embedded with a nanomechanical resonator is developed whose dynamics can be captured by the coupled-Van der Pol–Duffing equations. Activating the nanomechanical resonator can dispersively shift the micromechanical resonance by more than 100 times its bandwidth and concurrently increase its energy dissipation rate to the point where it can even be deactivated. The coupled-Van der Pol–Duffing equations also suggest the possibility of self-oscillations. In the limit of strong excitation for the nanomechanical resonator, the dissipation in the micromechanical resonator can not only be reduced, resulting in a quality factor of >3× 10⁶, it can even be eliminated entirely resulting in the micromechanical resonator spontaneously vibrating