Response of discrete nonlinear systems with many degrees of freedom
arXiv:cond-mat/0411008 · doi:10.1103/PhysRevE.73.016214
Abstract
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.
arXiv commentVersion 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
References in corpus (6)
- Noise-enabled precision measurements of a Duffing nanomechanical resonator
- Superconducting Qubit Storage and Entanglement with Nanomechanical Resonators
- Metastability and the Casimir Effect in Micromechanical Systems
- Response of parametrically-driven nonlinear coupled oscillators with application to micro- and nanomechanical resonator arrays
- Synchronization by Nonlinear Frequency Pulling
- Optical manipulation of intrinsic localized vibrational energy in cantilever arrays
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