Effective quality factor of mechanical resonators under complex-frequency excitations

We investigate the dynamics of mechanical resonators driven by excitations that include an oscillating or harmonic component with an amplitude that decays exponentially over time. We refer to these as complex-frequency excitations, and we show that the resulting response is quasisteady; 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 249-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 nanoelectromechanical sensors.