An efficient numerical solution for frequency response function of micromechanical resonator arrays

Array forms of MEMS resonator that uses a specific mid-frequency normal mode have been introduced for acquiring a wider bandwidth of frequency response function (FRF). A conventional frequency response solver based on a modal approach faces computational difficulties in obtaining the FRF of these array forms because of the increase in the order of a linear dynamic model and the number of retained normal modes. The computational difficulties can be resolved by using a substructuring-based model order reduction and a frequency sweep algorithm, which requires a smaller number of retained modes of a reduced dynamic system than the conventional solver. In computing the FRF of a single resonator and its array forms, the presented method shows much better efficiency than the conventional solution by ANSYS as the number of resonators increases. In addition, the effects of multiple resonators in the array forms on filter performance are discussed compared with experimental data.