Pattern selection in parametrically-driven arrays of nonlinear resonators

TL;DR

This paper investigates pattern selection in arrays of nonlinear resonators driven parametrically, revealing hysteretic transitions between standing-wave patterns and confirming findings through numerical simulations.

Contribution

It applies an amplitude equation to analyze pattern transitions in MEMS/NEMS resonator arrays, highlighting novel hysteretic effects not previously documented.

Findings

Identification of hysteretic pattern transitions

Confirmation of theoretical predictions via numerical simulations

Analysis of drive amplitude effects on pattern selection

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.