Application of pole allocation to optimize passive viscous dampers represented by the Maxwell model

The Maxwell model is used to understand the realistic effectiveness of vibration reduction in the building structures. The model consists of a dashpot and spring in series. The dashpot and spring represent a viscous damper and joint between the damper and the structural frame, respectively. However, few studies have investigated the optimal damper capacity and the corresponding spring stiffness in the practical parameter ranges. Additionally, the optimal damper derived using the fixed-point theory has no relationships with that derived via pole allocation. Therefore, in this study, to examine the effects of the joint spring, the pole allocation method was used to design a structural system wherein the Maxwell model was incorporated into a single-degree-of-freedom damped model. We introduced a closed-form expression, which explicitly described the relationships between the target structural damping ratio, damper capacity, and joint spring. The Maxwell model constrained the control effectiveness using damper parameters and simultaneously suggested an optimal and realistic joint spring for the damper. Pole allocation was also applied to a multi-degree-of-freedom (M-DOF) damped structural system employing multiple Maxwell models. The newly proposed optimized joint spring could easily control the additional damping effect on the M-DOF system. The Maxwell model can be optimized almost manually. The scheme is more useful in the preliminary design stage than the previous numerical optimizations. This study extended the mathematical equation governing the building vibrations to the Maxwell model. The extended equation served as a unified description for considering structural passive control.