Optimization of Anti-Resonance Peaks for Time-Delay Coupled Dynamic Vibration Absorbers with Inertial Containment

In this paper, a time delay is coupled to a dynamic vibration absorber with an inerter-based grounded stiffness that contains an amplification mechanism, and a model of the dynamic vibration absorber with time-delay feedback control containing an inerter is obtained. For this model, the vibration differential equation of the system is first established, and the optimal structural parameters of the passive system with an inerter are analyzed under the condition of no time delay. When the time delay is considered, the characteristic equation of the system is a transcendental equation with exponential terms. The CTCR method and the Dixon resultant are used to analyze the stability of the system, and the stable intervals of the feedback gain coefficient and time delay are obtained. Then, according to the anti-resonance peak optimization criteria, the structural parameters of the system are further adjusted under the condition of ensuring the system’s stability, and a set of optimal structural parameters is successfully obtained, which can not only meet the minimum anti-resonance peak criterion but also have a wider vibration reduction frequency band and a good vibration reduction effect. Finally, the optimization results are verified in both the time domain and the frequency domain. Compared with the traditional dynamic vibration absorber, the dynamic vibration absorber designed in this paper has achieved a good vibration reduction effect.