建物のパッシブ振動制御の極配置法に基づく統一的理解

Abstract

For a building with a passive control system, an inverse problem is formulated based on the pole allocation method in control theories. The structural system is simplified as a 3DOF damped lumped-mass shear model. The model can express an earthquake resistant structure, a base-isolated structure, an interstory-isolated structure, or a structure with a tuned mass damper or viscous dampers by changing its parameters adequately. The natural frequencies and the corresponding damping ratios in three vibration modes are set as the initial control target for performance-based design. The introduced closed-form expression explains how model parameters are related to the control target, and the mathematical expression generally proves the trade-off relationship in passive control effect. The relationship is extended to an MDOF damped-mass shear model. The numerical examples indicate that the pole allocation has arbitrariness in selecting a solution and a limited solution can be applied to the actual building.