Some fundamental properties are disclosed on eigenvibration and damping in connected building structures. A classification in terms of damping variation properties with respect to increased capacity of connected dampers is conducted by using complex eigenvibration analysis. There exist several regions in the plane of mass ratio and stiffness ratio. In each region, the lowest-mode damping variation exhibits a different property with respect to increased capacity of connected dampers. These properties are useful in the design of the system of connected buildings.
