Understanding the Quality Factor of Mass-Loaded Tensioned Resonators

TL;DR

This paper investigates how adding mass to tensioned mechanical resonators affects their mode shape and quality factor, revealing a saturation effect that is validated through analytical, numerical, and experimental methods.

Contribution

It introduces an analytical and finite element model showing mode shape independence from load mass and experimentally confirms the quality factor saturation in tensioned resonators.

Findings

Mode shape becomes independent of load mass at high loads

Quality factor saturates as load mass increases

Experimental validation with silicon nitride trampoline resonators

Abstract

Mechanical resonators featuring large tensile stress have enabled a range of experiments in quantum optomechanics and novel sensing. Many sensing applications require functionalizing tensioned resonators by appending additional mass to them. However, this may dramatically change the resonator mode quality factor, and hence its sensitivity. In this work, we investigate the effect of the crossover from no mass load to a large mass load on the mode shape and quality factor of a tensioned resonator. We show through an analytical model and finite element analysis that as the load mass increases, surprisingly, the resonator mode shape becomes independent of the exact load mass, and therefore, its quality factor saturates. We validate this saturation effect experimentally by measuring the quality factor of a silicon nitride trampoline resonator while varying the load mass in a controlled manner.