Effective quality factor of mechanical resonators under complex-frequency excitations

TL;DR

This paper introduces a method to determine the effective quality factor of mechanical resonators under complex-frequency excitations, enabling improved sensitivity and resolution without structural modifications.

Contribution

The authors present a novel approach to analyze resonator dynamics under complex-frequency excitations, linking steady-state responses to effective quality factors.

Findings

Numerical simulations confirm the method's validity.

Experiments show a 54-fold increase in effective quality factor.

The approach enhances detection sensitivity and sensor resolution.

Abstract

We investigate the dynamics of mechanical resonators subject to excitations comprising of an oscillating or harmonic part, whose amplitude decays exponentially in time. We call these complex frequency excitations and show that the resulting response is quasi-steady, i.e. after an appropriate transform, the response of the new variable corresponds to the steady state behavior under a harmonic excitation. A procedure is presented to determine the amplitude-frequency response and effective quality factor based on this steady-state behavior. Optimal excitations are identified for both single and multi-degree of freedom systems that result in the amplitude-frequency response approaching that of an undamped system. The feasibility of the proposed method is verified through numerical simulations. Experiments with cantilever beams made of acrylic show a 54-fold increase in the effective quality factor. Our method does not involve any structural modifications and opens avenues for improving detection sensitivity in nondestructive testing and enhancing resolution in micro- and nano-electromechanical sensors.