Modal Interaction in a Levitation Force MEMS Based Resonator

Abstract

This work aims to examine the possibility of internal resonances (modal interactions) among the vibration modes of a levitation force Micro-electro-mechanical Systems (MEMS) based resonator. The actuating levitation force is generated through a special arrangement consisting of two stationary side electrodes (both electrically charged) and a middle grounded unit consisting of the stationary electrode located beneath a moving electrode (micro-beam). Both “cantilever” (CL) and “clamped-clamped” (CC) microbeams are analysed as the moving element of this especial design in which the applied voltage pushes away the micro beam from the underneath substrate. All possible commensurable relations between the frequencies are inspected. We use the numerical bifurcation toolbox MatCont to capture the computed frequency response branches and examine their stability. A period-doubling bifurcation for the possible onset of chaotic attractors is inspected as well. A preliminary eigenvalue problem analysis suggests the internal resonance may exist in both (CC and CL) cases. However, an extended dynamical analysis shows that just a 3-to-1 modal interaction (between the first and third modes) in the CC arrangement is possible. The effects of dominant force-related terms are plotted through associated plots. These diagrams demonstrated that this design exhibits a rich internal resonance behavior that can be controlled with different geometrical and actuating parameters. Overall, this effort provides a systematic methodology and simple guidelines for indepth exploration of internal resonances in levitation force-based microbeams. The outcomes of this work could also assist in the development of MEMS sensors based on the internal resonance phenomenon.