Investigating Mode Localization at Lower- and Higher-Order Modes in Mechanically Coupled MEMS Resonators

Abstract

Mode localization is investigated in a weakly mechanically coupled system. The system comprises of two doubly clamped microbeams mechanically linked with a coupling beam close to the anchors. The phenomenon is explored among the first three vibration modes pairs, each consisting of an in-phase and out-of-phase mode. A distributed-parameter model accounting for the two mechanically coupled resonators, the coupling beam, and their geometric and electric nonlinearities are derived using the extended Hamilton's principle. A reduced-order model is then derived from the Lagrangian of the equations. An eigenvalue analysis is performed under different side electrode bias scenarios. The voltage bias impact on the natural frequencies of the pairs of modes is investigated. Veering among the various modes is observed and studied as varying the bias conditions. It is demonstrated that the veering zones can be greatly affected, tuned, and shifted by the biasing voltages. Finally, forced vibration analysis is performed. It is observed that the choice of the resonator to be excited, perturbed, and its response to be monitored is very important to fully understand and utilize the localization phenomenon for practical applications. Further, it is observed that very weak coupling is required to activate mode localization in higher-order modes. The reported selective localization and activation and deactivation of higher-order modes can be potentially useful for various applications, such as parallel mechanical computing, and for ultra-sensitive in high-frequency environments.