H_∞ optimization of a hybrid multiple-delayed delayed resonator vibration absorber

Delayed resonator (DR) as an active vibration absorber can achieve a zero antiresonance point of the primary structure at a given frequency by manipulating the loop delay, yielding the so-called complete vibration suppression. Achieving zero antiresonance, however, is usually penalized by the significantly raised resonance peaks, risking structural safety. Here, we aim to limit the resonance while achieving zero antiresonance, leading to the H_∞ optimization problem. To simplify analyses, we distinctively incorporate the primary structure-based feedback force into the total control forces of the DR and activate them only when residual vibrations occur. This reduces parametric coupling so that resonance peaks can be reduced without affecting zero antiresonance. Given the benefits of tuning delay from the DR concept itself, the states of the primary structure are also delayed in the feedback loop for additional performance enhancement, finally creating the so-called hybrid multiple-delayed DR. By analyzing system stability, characteristic spectrum, and frequency response, we show that pursuing an extremum reduction of resonance peaks can conflict with operable complete vibration suppression, thus requiring a trade-off between the two. Furthermore, by properly optimizing control parameters, both tasks can be significantly enhanced simultaneously. This work introduces a new design framework to enhance vibration suppression in terms of both resonance and antiresonance.