Fundamental equation based on pole allocation for interstory seismic isolation of buildings

Abstract

An inverse problem is formulated based on the pole allocation method in control theory, for a building with an interstory seismic isolation system. The structural system is simplified as a three-degree-of-freedom lumped-mass shear model. The natural frequencies and the corresponding damping ratios in the three vibration modes are set as the initial control target. To achieve this target, the introduced solution provides the natural frequencies of the lower substructure, upper substructure, and isolator with damper capacity. It simultaneously provides the mass distribution for the three lumped masses. The closed-form expression clarifies how the isolator's natural frequency and damper's capacity are related to the dominant natural frequencies of both the substructures and to the target modal damping ratios. The mathematical expression explains the trade-off relationship between the damping ratios of the lower and upper substructures. Furthermore, the solution is applied to directly estimate the damping effect by a tuned mass damper. The inverse problem approach is effective for understanding the general and essential dynamic characteristics of interstory seismic isolation.