Nonlinear damping in a micromechanical oscillator

TL;DR

This paper investigates nonlinear dissipation in micromechanical oscillators, revealing its significant impact on dynamics and proposing a viscoelastic model, while also highlighting the presence of additional nonlinear dissipative processes.

Contribution

It introduces a model combining nonlinear elastic and dissipative effects in MEMS oscillators and compares it with experimental data, emphasizing the importance of nonlinear dissipation.

Findings

Nonlinear dissipation significantly affects oscillator dynamics.

A viscoelastic model with Voigt-Kelvin dissipation relates linear and nonlinear damping.

Experimental results indicate additional nonlinear dissipative processes beyond the model.

Abstract

Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). 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 frequency domain and time domain and compared to theoretical predictions based on 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 nonlinear viscoelastic string with Voigt-Kelvin dissipation relation, which shows a relation between linear and nonlinear damping. However, the experimental results suggest that this model alone cannot fully account for all the experimentally observed nonlinear dissipation, and that additional nonlinear dissipative processes exist in our devices.