Dynamics of Globally and Dissipatively Coupled Resonators

Abstract

This work explores the dynamics of arrays of globally and dissipatively coupled resonators. These resonator arrays are shown to be capable of exhibiting seemingly new collective behaviors which are highly sensitive to the dispersion of the natural frequencies of the constituent resonators in the array, the intrinsic damping of the resonators in the array, and the magnitude of the global coupling coefficient that captures the strength of the dissipative coupling. These behaviors have been identified within the work as group attenuation, confined attenuation, and group resonance. Group and confined attenuation are associated with an absence of energy and are strongly dependent on the dispersion of the natural frequencies. In cases of moderate dissipative coupling, the effects of group and confined attenuation could be interpreted as frequencydependent damping. In cases where the global coupling coefficient is large, group resonance is significant. This effect is synonymous with the resonances of the constituent resonators being shared and occurring at frequencies in between the isolated resonators' natural frequencies. Accordingly, one could view group resonance as the antithesis of localization, in that the localization of the modes of a conservatively coupled system with a finite dispersion of the constituent resonators' natural frequencies is most significant when the coupling is weak. The authors believe that collective behaviors, such as those described herein, have direct applicability in new singleinput, singleoutput resonant mass sensors, and, with extension, a variety of other sensing and signal processing systems.