Real-Time Tuning of Delayed Resonator-Based Absorbers for Spectral and Spatial Variations

This paper offers two interlinked contributions in the field of vibration absorption. The first involves an active tuning of an absorber for spectral and spatial variations. The second contribution is a set of generalized design guidelines for such absorber operations. “Spectral” tuning handles time-varying excitation frequencies, while “spatial” tuning treats the real-time variations in the desired location of suppression. Both objectives, however, must be achieved using active control and without physically altering the system components to ensure practicality. Spatial tuning is inspired by the concept of “noncollocated vibration absorption,” for which the absorber location is different from the point of suppression. This concept is relatively under-developed in the literature, mainly because it requires the use of part of the primary structure (PS) as the extended absorber—a delicate operation. Within this investigation, we employ the delayed resonator (DR)-based absorber, a hybrid concept with passive and active elements, to satisfy both tuning objectives. The presence of active control in the absorber necessitates an intriguing stability investigation of a time-delayed dynamics. For this subtask, we follow the well-established methods of frequency sweeping and D-subdivision. Example cases are also presented to corroborate our findings.