Response of discrete nonlinear systems with many degrees of freedom

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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.
Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1, but no additional results

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Other Condensed Matter, Pattern Formation and Solitons

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http://salesiana.dossiersoluciones.com/handle/123456789/226261

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0411008
 http://arxiv.org/abs/cond-mat/0411008
 Phys. Rev. E 73, 016214 (2006)
 doi:10.1103/PhysRevE.73.016214

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arXiv