In a strongly driven nanomechanical mode, ring-down in the rotating frame is non-exponential: the in-phase component initially decays at about twice the rate of the quadrature, as a Duffing model with a dominant second harmonic predicts.
A Generic Rotating-Frame-Based Approach to Chaos Generation in Nonlinear MEMS NEMS Resonators
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abstract
This work provides a low-power method for chaos generation which is generally applicable to nonlinear M/NEMS resonators. The approach taken is independent of the material, scale, design, and actuation of the device in question; it simply assumes a good quality factor and a Duffing type nonlinearity, features that are commonplace to M/NEMS resonators. The approach models the rotating-frame dynamics to analytically constrain the parameter space required for chaos generation. By leveraging these common properties of M/NEMS devices, a period-doubling route to chaos is generated using an order-of-magnitude smaller forcing than typically reported in the literature.
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Non-Exponential Relaxation in the Rotating Frame of a Driven Nanomechanical Mode
In a strongly driven nanomechanical mode, ring-down in the rotating frame is non-exponential: the in-phase component initially decays at about twice the rate of the quadrature, as a Duffing model with a dominant second harmonic predicts.