Frequency tuning of weakly and strongly coupled micromechanical beams

Abstract

Mechanical coupling forms the basis for many exciting applications in tuning the frequencies of multi-degrees of freedom systems starting from coupling the motion of fire-flies to MEMS arrays. In this paper, the influence of the weak and strong coupling between two micromechanical cantilever beams is performed using the experimental and analytical studies. To do the study, the two types of coupled micromechanical beams are taken, namely, a weakly coupled beams and a strongly coupled beams. While the weakly coupled beams are coupled along their lengths through a coupling beam of constant length and width, two strongly coupled beams are coupled through beams of varying length and constant width with one end of its length fixed at fixed portion of cantilever beam. Here, we fabricated both types of coupled beams through microfabrication process. After measuring their in-phase and out-of-phase frequencies with varying coupling parameters, the influence of coupling parameters on these two modes is investigated. It is found that one of the modes consist of a transverse mode and another a kind of torsional mode which lead to out-of-phase mode. After finding this interesting observation, further analysis is done using the corresponding analytical models of transverse and torsional modes. Furthermore, the generalized analytical models are developed to capture the effects of coupling in weakly and strongly coupled beams as a function of coupling element dimensions.