Real-time tunable single-degree of freedom, multiple-frequency vibration absorber

Typically single-mass absorbers combat a single excitation frequency at a time. In this paper we explore a novel control scheme to handle multiple and time-varying frequencies, but again using a single-mass absorber. The key scientific contribution is in the new way the spectral sensitivity is induced to the absorber substructure at multiple frequencies. This tuning process is achieved using a novel extension to the conventional Delayed Resonator (DR) concept with several delays. We show that the method can track all frequencies in real time. Therefore the new conception dramatically expands the traditional fixed-frequency absorption operations, for instance Dual Frequency Fixed Delayed Resonator (DFFDR). On-line deployment starts with a selection of a base delay in the feedback control on a given passive absorber. Necessary feedback gains for proper tuning are evaluated and control decision is made in real time. The stability repercussions of this control law, however, need to be assessed in advance. For this we use a recent characteristic root approximation method, QPmR (Quasi-Polynomial Mapping Based Root finding). These assessments create some restrictions for tunable frequency ranges with guaranteed stability. Such limitations, as well as the practical complexities of the new tuning method are also discussed over an example case study.