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.

中文翻译：

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基于极点分配的基础层间建筑物隔震基本方程

基于控制理论中的极点分配方法，针对具有层间隔震系统的建筑物，提出了一个反问题。结构系统简化为三自由度集总质量剪切模型。将三种振动模式下的固有频率和相应的阻尼比设置为初始控制目标。为了实现此目标，引入的解决方案为下部子结构，上部子结构和隔离器的固有频率提供了阻尼能力。同时提供三个集总质量的质量分布。封闭形式的表达式阐明了隔振器的固有频率和阻尼器的能力如何与子结构的主要固有频率以及目标模态阻尼比有关。数学表达式解释了下部和上部子结构的阻尼比之间的权衡关系。此外，该解决方案适用于通过调谐质量阻尼器直接估算阻尼效果。反问题方法对于理解层间地震隔离的一般和必要的动力特性是有效的。