Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays

By R. Lifshitz, Michael Cross. 2002

162 citations recorded by the source corpus.

The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, J. Microelectromech. Syst. 11, 802 (2002)] involving a parametrically excited micromechanical resonator array. Future experiments are suggested which could provide quantitative tests of the theoretical predictions.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/fb0d804bea2fa24ceec3729efede6bc077df3aec

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In Atomic and Molecular Physics, and Optics

In Electrical and Electronic Engineering

Citations in the corpus

Nonlinear damping in a micromechanical oscillator (2009, background): “As will be shown below, this approach is equivalent to the case where the damping nonlinearity is proportional to the velocity cubed [64].”
Nonlinear Dynamic Analysis of Electrostatically Actuated Resonant MEMS Sensors Under Parametric Excitation (2007, background): “Lifshitz and Cross [16] presented the theoretical study of the phenomena of parametric excitation in spatially extended MEMS/NEMS.”
Electrically tunable collective response in a coupled micromechanical array (2002, methodology): “To account for these observations, Lifshitz and Cross [ 15 ] have developed recently a theoretical model of the system presented in this work.”