Study of the non-linear dynamics of micro-resonators based on a Sn-whisker in vacuum and at mK temperatures

TL;DR

This study investigates the non-linear dynamics of Sn-whisker micro-resonators at cryogenic temperatures using both frequency and time domain methods, demonstrating their behavior aligns with Duffing oscillator theory.

Contribution

It provides a comprehensive analysis of Sn-whisker micro-resonators' non-linear behavior, combining experimental measurements with theoretical modeling based on the Duffing oscillator.

Findings

Dynamics are well-described by Duffing's model

Experimental results match theoretical predictions

Insights into intrinsic mechanical properties at mK temperatures

Abstract

The dynamics of micro-resonators (or any mechanical resonators) can be studied by two complementary methods allowing the measurements in two different domains: (i) in the frequency domain - by the frequency sweeps using cw-excitation, and (ii) in the time domain - by the pulse techniques, when the free-decay oscillations are investigated. To broaden the knowledge about the intrinsic mechanical properties of micro-resonators based on a Sn-whisker we used both methods. We show that the dynamics of the Sn-whisker can be described by a phenomenological theory of the Duffing oscillator. Furthermore, we present the results of theoretical analysis based on the Duffing's model provided in the time and frequency domains, and we show that these results are qualitatively the same with those measured experimentally.