Actively Tuned Noncollocated Vibration Absorption: An Unexplored Venue in Vibration Science and a Benchmark Problem

We revisit actively tuned vibration absorbers in this article from several unconventional angles. First, the absorber exacts suppression at a designated location in the structure other than its point of attachment (thus, noncollocated suppression). Second, it is tunable to suppress all residual oscillations at that point against a harmonic excitation, thus overriding all modal characteristics. Furthermore, the tuning is achieved in real time, using a collocated control logic with a feedback gain and delay. Although this combination of vibration absorption characteristics can be achieved using various control designs, the well-studied delayed resonator (DR) concept is utilized in this article. Asymptotic stability of the ensuing dynamics is examined in the parametric space, and operable frequency limitations are explored. A paradoxical relationship is noted between the steady-state energy levels, which may occur for passive and actively tuned absorber cases. This phenomenon provides an intriguing benchmark problem. All of these contributions are clarified over a case study.