Pattern selection in parametrically-driven arrays of nonlinear resonators

Abstract

We study the problem of pattern selection in an array of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS & NEMS), using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [PRE 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude is varied either quasistatically, abruptly, or as a linear ramp in time. We find novel hysteretic effects, which are confirmed by numerical integration of the original equations of motion of the interacting nonlinear resonators.

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• Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators
• Logic Operations Demonstrated with Localized Vibrations in a Micromechanical Cantilever Array