Response of discrete nonlinear systems with many degrees of freedom

Details Response of discrete nonlinear systems with many degrees of freedom Response of discrete nonlinear systems with many degrees of freedom

2004-10-30

arxiv.org/abs/cond-mat/0411008v2

Phys. Rev. E 73, 016214 (2006)

Physics

Condensed Matter

Other Condensed Matter

Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1,

Scientific paper

10.1103/PhysRevE.73.016214

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wavenumber dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators.

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