Mode coupled vibration in distributed driven T-shaped MEMS resonant systems

Mode coupled vibration plays an important role in improving the dynamic performance of MEMS resonators and broadening the application range of micro-resonant devices. However, the mode coupled vibration behavior depends heavily on the natural frequency and nonlinear stiffness of MEMS resonators. In this study, a distributed electrostatic driven T-shaped resonant structure with 1:2 internal resonance potential is designed and fabricated for the first time, which can realize the modulation of mode coupled vibration by introducing multiple electrodes. Firstly, the effects of distributed driving voltage on natural frequency and dynamic behavior are measured experimentally. When the control voltage is between 210 V and 225 V, the resonator may have obvious mode coupled vibration phenomenon. Through perturbation and bifurcation analysis, the physical conditions of mode coupled vibration are deduced theoretically. It is interesting to note that both stiffness hardening and stiffness softening occur in T-shaped resonators. The mode coupled vibration phenomenon occurs twice from forward and reverse frequency sweeps. Typically, the double mechanical frequency locking induced by the transfer of vibration energy from higher mode to lower mode is measured experimentally. As the AC driving voltage increases, the resonator has obvious peak frequency stability intervals, which greatly improves the robustness of the peak frequency. Besides, the influence of vacuum degree on the mode coupled vibration behavior is also measured experimentally and predicted theoretically. With the decrease of vacuum degree, the critical driving voltage of mode coupled vibration increases obviously, which provides a new idea for the detection of vacuum degree.