Response of parametrically-driven nonlinear coupled oscillators with application to micro- and nanomechanical resonator arrays

TL;DR

This paper analyzes the behavior of coupled nonlinear oscillators under parametric excitation, using perturbation theory and numerical simulations, to explain recent experimental results in micro- and nanomechanical resonator arrays.

Contribution

It provides a theoretical framework for understanding parametric excitation in nonlinear oscillator arrays, connecting analytical results with experimental observations.

Findings

Qualitative explanation of experimental results

Guidance for future experiments

Analysis of small and large oscillator arrays

Abstract

The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)] involving a parametrically-excited micromechanical resonator array. Future experiments are suggested that could provide quantitative tests of the theoretical predictions.