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

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

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 R...

Classical to quantum transition of a driven nonlinear nanomechanical resonator

Much experimental effort is invested these days in fabricating nanoelectromechanical systems (NEMS) that are sufficiently small, cold and clean, so as to approach quantum mechanical behavior as their typical quantum energy scale h̄ becomes comparable with that of the ambient thermal energy kBT . Such systems will hopefully enable one to observe the quantum behavior of human-made objects, and te...

Nonlinear Dynamics of Nanomechanical and Micromechanical Resonators

Intrinsic localized modes in parametrically driven arrays of nonlinear resonators.

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-L...

Pattern selection in parametrically driven arrays of nonlinear resonators.

We study the problem of pattern selection in an array of parametrically driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems, using an amplitude equation recently derived by Bromberg, Cross, and Lifshitz [Phys. Rev. E 73, 016214 (2006)]. We describe the transitions between standing-wave patterns of different wave numbers as the drive amplitude...