Nonlinear damping in a micromechanical oscillator

Abstract

Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). A Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast, nonlinear dissipation effects in micromechanical oscillators are often overlooked. In this work, we consider a doubly clamped micromechanical beam oscillator, which exhibits nonlinearity in both elastic and dissipative properties. The dynamics of the oscillator is measured in both frequency and time domains and compared to theoretical predictions based on a Duffing-like model with nonlinear dissipation. We especially focus on the behavior of the system near bifurcation points. The results show that nonlinear dissipation can have a significant impact on the dynamics of micromechanical systems. To account for the results, we have developed a continuous model of a geometrically nonlinear beamstring with a linear Voigt-Kelvin viscoelastic constitutive law, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account forall the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.

Methods for Atomistic Simulations of Linear and Nonlinear Damping in Nanomechanical Resonators

“…In other words, the structure can be driven into the nonlinear regime simply by requiring the harmonic response to be significantly greater than the thermal noise. Furthermore, the frequency response displayed the characteristic signatures of the Duffing-like nonlinearity, as also observed in experimental studies of nonlinear damping in micromechanical and nanomechanical resonators [20], [35]- [38].…”

Symmetry breaking in a mechanical resonator made from a carbon nanotube

“…4c. A general theory that incorporates nonlinearities in both the restoring force and damping 10,[23][24][25][26] as well as thermal vibrations is beyond the scope of this article. We note that our new technique to measure the motion of the equilibrium position allows one to study the response of the resonator over a broad parameter range in driving force.…”

Parametric Amplification and Back-Action Noise Squeezing by a Qubit-Coupled Nanoresonator

“…up to the second order of x , we can identify higher order terms such as We note that, from the fluctuation-dissipation theorem, this nonlinear dissipation should have been accompanied by displacement-dependent terms in the nanoresonator's force noise correlation 4 . However, we did not attempt to measure this force noise correlation in the current experiment.…”