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Response of discrete nonlinear systems with many degrees of freedom

Bromberg, Yaron and Cross, M. C. and Lifshitz, Ron (2006) Response of discrete nonlinear systems with many degrees of freedom. Physical Review E, 73 (1). Art. No. 016214. ISSN 1063-651X. doi:10.1103/PhysRevE.73.016214.

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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 wave-number 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.

Item Type:Article
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Lifshitz, Ron0000-0002-8829-5506
Additional Information:©2006 The American Physical Society. Received 30 October 2004; published 18 January 2006. This research is supported by the U.S.-Israel Binational Science Foundation (BSF) under Grants No. 1999458 and 2004339, the National Science Foundation under Grant No. DMR-0314069, and the PHYSBIO program with funds from the EU and NATO.
Subject Keywords:nonlinear dynamical systems; oscillators; micromechanical resonators; bifurcation
Issue or Number:1
Record Number:CaltechAUTHORS:BROpre06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3785
Deposited By: Tony Diaz
Deposited On:10 Jul 2006
Last Modified:08 Nov 2021 20:12

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