Modal Behavior of Microcantilevers Arrays with Tunable Electrostatic Coupling

Abstract

We analyse the spectral content and parametric resonant dynamics of an array of elastically and electrostatically coupled interdigitated micro cantilevers assembled into two identical half-arrays. In this uncommon arrangement, within each of the half-arrays, the beams are coupled only elastically. The half-arrays are intercoupled only electrostatically, through fringing fields. First, by using the reduced order (RO) model, we analyse the voltage-dependent evolution of the eigenvalues and the eigenvectors of the equivalent mass-spring system, starting from the small two, three and four beams arrays and up to large beams assemblies. We show that at the coupling voltages below a certain critical value, the shape of the eigenvectors, the frequencies of the veering and of the crossing are influenced by the electrostatic coupling and can be tuned by the voltage. Next, by implementing the assumed modes techniques we explore the parametric resonant behavior of the array. We show that in the case of the sub critical electrostatic coupling the actuating voltages required to excite parametric resonance in the damped system can be lower than in a strongly coupled array. The results of the work may inspire new designs of more efficient resonant sensors.