Localization in Microresonator Arrays: Influence of Natural Frequency Tuning

Intrinsic localized modes are localization events caused by intrinsic nonlinearities within an array of perfectly periodic coupled oscillators. Recent developments in microscale fabrication techniques have allowed for the studies of this phenomenon in micro-electromechanical systems. Studies have also identified a relationship between the spatial profiles of intrinsic localized modes and forced nonlinear vibration modes, as well as a potential sensitivity to fundamental frequency relationships of one-to-one and three-to-one between adjacent oscillators. For the system considered, the one-to-one frequency relationship is determined to provide nonideal conditions for studying intrinsic localized modes. The influence of the three-to-one frequency relationship on the behavior of the intrinsic localized modes is studied with analytical methods and numerical simulations by tuning the fundamental frequencies of the oscillators. While the perfect tuning condition is not determined to produce a unique phenomenon, the number and energy concentration of the localization events are found to increase with the increased frequency ratio, which results in a decrease in the effective coupling stiffness within the array.

Internal Resonance and Localization in Micro-Resonator Arrays

Intrinsic Localized Modes (ILMs) are localization caused by intrinsic nonlinearities within an array of perfectly periodic oscillators. This localization phenomenon is studied in the context of arrays of coupled micro-scale cantilevers and of coupled piezoelectric micro-scale resonators. Recent studies have identified the individual devices to be capable of producing nonlinear behavior and efforts are currently underway to develop resonator arrays to improve performance capabilities. It is important to determine whether an ILM would limit the performance of such an array and/or if one could take advantage of this type of localization in filter design. Previous studies have shown that it is possible to realize ILMs as forced nonlinear vibration modes. The effects of internal resonance conditions on the behavior of these localization events are explored here using analytical and numerical methods.