Stability Analysis of the Acceleration-based Delayed Resonator with Virtual Natural Frequency

The acceleration-based Delayed Resonator (DR) is known for its ideal vibration suppression and simple achievement. However, the instability when treating low-frequency vibrations, and the steep decline in the required delay control parameter when suppressing high-frequency ones greatly limits its practical usages. As a modification, we further study a novel DR control strategy based on the virtual adjustment of the natural frequency of the DR itself, with the hope to extend the operable frequency range. The complete stability analyses of both the DR and coupled system are presented using the Cluster Treatment of Characteristic Roots (CTCR) paradigm. The results turn out that, this novel type of DR exhibits excellent applicability in the low-frequency band, prolongs the delay parameters in the high-frequency band, and enhances robustness. Numerical comparisons and verifications are also included.