Non-Collocated Vibration Suppression with Actively Controlled Resonant-Style Absorbers for Simultaneous Spectral and Spatial Tuning

The research summarized in this work revisits the well-established actively-tuned vibration absorber concept from several unconventional angles. The first contribution involves an active tuning methodology of an absorber for spectral and spatial variations. The second is a set of generalized operating guidelines for such absorber tuning. Spectral tuning handles time-varying excitation frequencies, while spatial tuning treats the real-time variations in the desired location of suppression (an often-ignored dimension of vibration absorption research). Spatial tuning is inspired by the concept of “non-collocated vibration absorption”, for which the absorber location is different from the point of suppression. The Delayed Resonator-based absorber, a hybrid concept with passive and active elements, is employed 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, the well-established methods of frequency sweeping and D-subdivision are followed. The non-collocated vibration absorption is demonstrated via several example case studies on lumped-mass structures, which consequently leads to the presentation of simultaneous spectral and spatial tuning. This operation has intriguing properties which can be optimized to reduce fatigue in the structure. Additionally, an important theorem is introduced, and two different proofs are offered. Then, the extension from discrete to continuous structures is made by attempting an analogous implementation of non-collocated suppression on an Euler-Bernoulli beam. This proves unsuccessful, but brings to light an important dichotomy between the beam and the lumped-mass structures. Several examples are presented to aid future researchers in attacking this benchmark problem