Article

Intrinsic localized modes in parametrically driven arrays of nonlinear resonators

Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel.
Physical Review E (Impact Factor: 2.29). 10/2009; 80(4 Pt 2):046202. DOI: 10.1103/PhysRevE.80.046202
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ABSTRACT

We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schrödinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction of ILMs, show that they can form bound states, and that under certain conditions one ILM can split into two. Our findings are confirmed by simulations of the underlying equations of motion of the resonators, suggesting possible experimental tests of the theory.

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Available from: Boris A. Malomed, Nov 05, 2014
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    • "By following the method of multiple scale expansion presented in [1], one can show that the considered model is an amplitude equation for the arrays of parametrically driven damped nonlinear oscillators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS) resonators [2], which is modelled by¨ϕ n = D(ϕ n+1 − 2ϕ n + ϕ n−1 ) − [ "
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    • "The analysis and the experiments reveals the existence of Intrinsic Localized Modes (ILMs), similar to those found in other more generic systems of nonlinearly vibratory lattices. The observation of ILM in 1D chain of coupled oscillators [11], [12], presenting many similarities with the discrete bubble model, showed to play a role in creating spatio-temporal localized excitations leading to the breaking of the bubble. In our periodic pendulum lattice apparatus describing the macroscopic equivalence of the bubble, the system parametrically driven at 5.4 Hz presents subharmonic behavior and localized modes oscillating at 2.7 Hz. Versus the amplitude and the frequency of the driving, the mechanical ring presents parametric instability surface modes and localized modes oscillating at subharmonics of the parametric excitation (see multimedia files and http://ultrasonsinserm .med.univ-tours.fr/aTelecharger/sDos/SergeMovies/ "

    Full-text · Dataset · May 2014
  • Source
    • "The analysis and the experiments reveals the existence of Intrinsic Localized Modes (ILMs), similar to those found in other more generic systems of nonlinearly vibratory lattices. The observation of ILM in 1D chain of coupled oscillators [11], [12], presenting many similarities with the discrete bubble model, showed to play a role in creating spatio-temporal localized excitations leading to the breaking of the bubble. In our periodic pendulum lattice apparatus describing the macroscopic equivalence of the bubble, the system parametrically driven at 5.4 Hz presents subharmonic behavior and localized modes oscillating at 2.7 Hz. Versus the amplitude and the frequency of the driving, the mechanical ring presents parametric instability surface modes and localized modes oscillating at subharmonics of the parametric excitation (see multimedia files and http://ultrasonsinserm .med.univ-tours.fr/aTelecharger/sDos/SergeMovies/ "
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