Simple modeling of self-oscillation in Nano-electro-mechanical systems

Source: arXiv


We present here a simple analytical model for self-oscillations in nano-electro-mechanical systems. We show that a field emission self-oscillator can be described by a lumped electrical circuit and that this approach is generalizable to other electromechanical oscillator devices. The analytical model is supported by dynamical simulations where the electrostatic parameters are obtained by finite element computations. Comment: accepted in APL

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Available from: Paul Manneville, Jan 18, 2014
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    • "Using the full slow envelope evolution equations, we derive the expressions governing the amplitudes and frequencies of all limit cycles [38] that exist in the system. The resulting steady state amplitude equations have the same form as those derived in literature from general power or force balance considerations [23] [29] [39] [40]. However, in this work, we are able to formulate the full evolution equations. "
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    ABSTRACT: The dynamical behavior of a nonlinear micromechanical resonator acting as one of the mirrors in an optical resonance cavity is investigated. The mechanical motion is coupled to the optical power circulating inside the cavity both directly through the radiation pressure and indirectly through heating that gives rise to a frequency shift in the mechanical resonance and to thermal deformation. The the energy stored in the optical cavity is assumed to follow the mirror displacement without any lag. In contrast, a finite thermal relaxation rate introduces retardation effects into the mechanical equation of motion through temperature dependent terms. Using standard averaging and harmonic balance techniques, slow envelope evolution equations are derived. In the limit of small mechanical vibrations, the micromechanical system can be described as a nonlinear Duffing-like oscillator. Coupling to the optical cavity is shown to introduce corrections to the linear dissipation, the nonlinear dissipation and the nonlinear elastic constants of the micromechanical mirror. The magnitude and the sign of these corrections depend on the exact position of the mirror and on the optical power incident on the cavity. In particular, the effective linear dissipation can become negative, causing self-sustained mechanical oscillations to occur. The full slow envelope evolution equations are used to derive the amplitudes and the corresponding oscillation frequencies of different limit cycles, and the bifurcation behavior is analyzed in detail. Finally, the theoretical results are compared to numerical simulations using realistic values of different physical parameters, showing a very good correspondence.
    Nonlinear Dynamics 04/2011; 69(4). DOI:10.1007/s11071-012-0371-9 · 2.85 Impact Factor