Anomalous dissipation of nanomechanical modes going through nonlinear resonance

TL;DR

This paper investigates nonlinear resonance in nano-mechanical systems, revealing anomalous dissipation behaviors and multiple steady-state vibration branches in coupled modes, especially near 1:3 resonance conditions.

Contribution

It provides analytical insights into the nonlinear resonance phenomena, including anomalous decay rates and stability of vibrations in nano-mechanical modes.

Findings

Decay rate of low-frequency mode depends nonmonotonically on amplitude.

Multiple steady-state vibration branches can exist near resonance.

Weak driving stabilizes strongly nonsinusoidal oscillations.

Abstract

We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the anomalously strong and nonmonotonic dependence of the decay rate of the low frequency mode on its amplitude, if the decay rate of the high-frequency mode is comparatively large. In this case the low-frequency mode driven close to resonance can have several branches of steady-state vibrations with constant amplitude. If the decay rates of the both modes are small compared to their coupling and internal nonlinearity, the dynamics corresponds to slowly decaying strongly nonsinusoidal oscillations of the vibration amplitude. Weak driving can make these vibrations stable.