Parametrically Excited Electrostatically Coupled Micro Oscillators

Resonant micro- and nanoelectromechanical (MEMS/NEMS) devices find application in biological and chemical sensors, scientific instruments allowing extremely precise material characterization and high-end timing and navigation measurement units for aerospace and defense applications. By monitoring the resonant frequencies of these structures, the parameters of interest could be extracted with high accuracy. Nonlinear dynamic phenomena, which are abundant in micro and nano devices due to presence of intrinsically nonlinear interaction forces, become an important and intensively investigated topic in the MEMS/NEMS arena. The reason of this interest is twofold. In micro structures, different types of nonlinearities could be easily tailored or even tuned in real time in order to enhance performance and meet specific application requirements. On the other hand, micro oscillators interacting by nonlinear forces exhibit rich dynamic behavior. In this prospective, micro technology can be viewed as a convenient platform for the theoretical and experimental exploration of this kind of systems. Among various types of devices, parametrically excited structures are attractive for implementation in sensors due to their ability to generate large resonant responses in a wide band of excitation frequencies as well as sharp transition between low-amplitude to large-amplitudes vibrations accompanying changes in system parameters. In this talk, several approaches to achieve parametric excitation in micro oscillators will be first reviewed. An excitation by direct stiffness modulation, excitation by means of inertia modulation as well as operation by fringing electrostatic fields will be presented. Distinguished features and possible applications of each of the approaches will be discussed. Next, results of theoretical and experimental investigation of the collective dynamic behavior of large arrays of micro oscillators will be presented. The device fabricated from the silicon on insulator substrates is consisting of two sets of partially interdigitated cantilevers. The adjacent beams are coupled mechanically due to clamping compliances, and electrostatically through voltage-dependent fringing fields. In the framework of the reduced order model built using Galerkin decomposition the array is considered as an assembly of single degree of freedom oscillators. Both local and non-local mechanical interactions are accounted for. The out-of-plane resonant responses are visualized by time-averaged temporally aliased video imaging and measured by laser Doppler vibrometry. We show that large amplitude collective vibrations of the array can be achieved using parametric excitation while the dynamic properties of the array such as the width of the propagation band as well as the modal patterns can be efficiently tuned by the applied voltage. Our experimental and model results collectively demonstrate that under a slowly varying drive frequency the standing wave patterns remain synchronized in certain frequencies intervals, followed by an abrupt change in the pattern. The ability to control the spectral characteristics using voltage can be useful for individual addressing of different locations of the sensing arrays, in band-pass filters with tunable passband and in diffractive optical devices.