Frequency latching in nonlinear micromechanical resonators

The resonance frequency of a nonlinear micromechanical resonator has a dependence on its modal amplitude known as the A–f effect. Here, we experimentally demonstrated that the A–f effect can be limited by the mode interaction in micromechanical resonators. The clamped-clamped beam resonator investigated in this work has a nonlinear in-plane (IP) vibration mode and a linear out-of-plane (OOP) vibration mode. In the case of single ended driving with various V_dc, the resonance frequency of the IP mode tuned through the A–f effect reaches that of the OOP mode and is limited by the OOP mode due to the modal interaction and electrostatic softening effect. In the case of double ended driving, however, the resonance frequency of the IP mode is latched to that of the OOP mode after A–f tuning and a frequency stabilized region is observed. A theoretical model is also put forward to explain this phenomenon through numerical simulations.