Dynamical Analysis and Optimization of Combined Vibration Isolator with Time Delay

Vibration control has long been a key concern in engineering, with low-frequency vibration isolation remaining particularly challenging. Traditional linear isolators are limited in their ability to provide high load-bearing capacity and effective low-frequency isolation simultaneously. In contrast, quasi-zero stiffness (QZS) isolators offer low dynamic stiffness near equilibrium while maintaining high static stiffness, thereby enabling superior isolation performance in the low and ultra-low frequency range. This paper proposes a novel vibration isolation system that combines a grounded dynamic absorber with a QZS isolator, incorporating time-delay feedback control to enhance performance. The dynamic equations of the system are derived using Newton’s second law. The harmonic balance method combined with the arc-length continuation technique is employed to obtain steady-state responses under harmonic force excitation. The influence of feedback gain and time delay on vibration isolation effectiveness and dynamic behavior is analyzed, demonstrating the ability of time-delay feedback to modulate system responses and suppress primary resonance peaks. To further enhance performance, a genetic algorithm is used to optimize the control parameters under harmonic force excitation. The force transmissibility is defined as fitness functions, and the effects of control parameters on these metrics are examined. The results show that the optimized time-delay feedback parameters significantly reduce the transmitted force, improving the overall isolation efficiency. The proposed system provides a promising approach for achieving high-performance vibration isolation in low-frequency environments.