Localization in Microresonator Arrays: Influence of Natural Frequency Tuning

Abstract

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.