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

摘要

The response of a coupled array of nonlinear oscillators to parametricexcitation is calculated in the weak nonlinear limit using secular perturbationtheory. Exact results for small arrays of oscillators are used to guide theanalysis of the numerical integration of the model equations of motion forlarge arrays. The results provide a qualitative explanation for a recentexperiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)]involving a parametrically-excited micromechanical resonator array. Futureexperiments are suggested that could provide quantitative tests of thetheoretical predictions.