Analytical Optimization Analysis of Inerter-Based Vibration Absorbers with Negative Stiffness

Traditional optimal design of NS-DVAs (Negative stiffness- dynamic vibration absorbers) is based on an extension of fixed-point approach, which equalizes the triple fixed points of the dynamic amplification function (DAF) to achieve approximate analytical H∞ optimization for dynamic reduction. However, this leads to stiffness matrix anomalies, resulting in a significant static amplification effect. For vibrations excited combining static and dynamic components, the static amplification may lead to adverse control effect, or even magnify the peak response, particularly, wind load. In order to solve these problems, an analytical optimal design approach for inerter-based vibration absorbers (IVAs) with NS (NS-IVAs) is proposed for balancing static amplification and dynamic reduction effects. Firstly, the characteristics of static amplification and dynamic reduction factors are analyzed. Subsequently, the relationship between the negative stiffness parameter and dynamic-static proportion is empirically formulated for practical application. Finally, the results of the numerical examples for wind-induced vibration control have shown that the proposed approach is particularly effective for the excitations dynamically characterized by low frequency and mixed with static components.