Dynamic relaxation oscillations in a nonlinearly driven quartz crystal

TL;DR

This paper reports on thermo-mechanical relaxation oscillations in a driven quartz crystal, revealing how thermal feedback induces low-frequency amplitude modulations through dynamic bifurcation.

Contribution

It introduces a simple model explaining thermally-induced relaxation oscillations in quartz crystals driven far from equilibrium.

Findings

Observation of two stable oscillation states with distinct impedance.

Oscillation frequency is about a million times lower than the resonance frequency.

Oscillation frequency can be tuned by detuning from the bifurcation point.

Abstract

We demonstrate thermo-mechanical relaxation oscillations in a strongly driven quartz crystal. Dynamic bifurcation leads to two stable oscillation states with a distinct electrical impedance. Slow Joule-heating, which shifts the susceptibility of the crystal, provides a feedback that leads to thermally-induced oscillations, in which the amplitude of the crystal is modulated by a relaxation cycle. The frequency of the relaxation cycle is roughly a million times lower than the resonance frequency of the crystal, and it can be adjusted by the detuning from the critical point for dynamic bifurcation. The experimental observations are reproduced by a simple model that takes into account the slow dynamics of the system.