Analytical optimization of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) using a reduced 2-degree-of-freedom (2DOF) model

Abstract

The incorporation of an inerter, with its mass amplification capability, along with a negative stiffness spring characterized by high static-low dynamic stiffness, can significantly enhance the vibration control performance of traditional tuned mass dampers (TMDs). The previous analytical solution for the optimal parameters of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) is a generalized single-degree-of-freedom (GSDOF) model with INDVAs attached. When utilizing INDVAs for controlling wind-induced responses in high-rise buildings, the accuracy of the GSDOF model is compromised. Therefore, a multi-degree of freedom (MDOF) model is initially reduced to a simplified 2-degree of freedom (2DOF) model using a clustering algorithm in this study. The H-∞ optimization method is then employed to derive simplified analytical solutions for the optimal parameters of the three types of INDVAs. The robustness of the parameters and the control effect of these optimal INDVAs are subsequently compared with those of numerical solutions generated through a multiobjective genetic algorithm and with those of analytical solutions based on the GSDOF model. The results demonstrate that for the same type of INDVA, compared with the multiobjective genetic algorithm, the optimal INDVA calculated by the 2DOF model can achieve the same control effect on the structural wind-induced response, while the time cost is lower. In addition, the optimal INDVA obtained by the 2DOF model has a superior control effect on the wind-induced displacement and acceleration response compared to those of the GSDOF model, especially when the INDVA has a substantial inertance ratio and spans multiple floors.