Exploring Operational Frequency Ranges for Actively-Tuned Single-Mass, Multiple-Frequency Vibration Absorber

A recent idea of developing an active control method over a single-mass tunable absorber is further explored in this study. Typically single-mass absorbers are designed to handle a single excitation frequency. In this paper, we explore a novel control scheme to actively tune such an absorber to multiple frequencies concurrently. The game changer is the way we induce the spectral sensitivity to the absorber substructure. This sensitivity (a.k.a. tuning) of the absorber is achieved following the core idea of Delayed Resonator (DR) except a novel feedback control with multiple delays. We show that this method can tune the absorber to all the intended frequencies in real time. Therefore the new concept dramatically expands over the fixed-frequency absorption operations, for instance Dual Frequency Fixed Delayed Resonator (DFFDR) ©. We start the operation with a feedback control using a predetermined delay over a given passive absorber. Necessary control gains for proper tuning are evaluated vis-à-vis the tuning frequencies. The stability of the dynamics therefore depends directly on the selection of these frequencies. This study is anchored on the discovery of the potential stability regions in the domain of the frequencies using a numerical root finding tool, QPmR (Quasi-Polynomial Mapping Based Root finding). Most important highlight of the paper is to demonstrate that there can be multiple regions on the frequency space for stable MFDR. The results obtained are cross validated by selected dynamic simulation over an example case study.