Design of passive interconnections in tall buildings subject to earthquake disturbances to suppress inter-storey drifts

This paper studies the problem of passive control of a multi-storey building subjected to an earthquake disturbance. The building is represented as a homogeneous mass chain model, i.e., a chain of identical masses in which there is an identical passive connection between neighbouring masses and a similar connection to a movable point. The paper considers passive interconnections of the most general type, which may require the use of inerters in addition to springs and dampers. It is shown that the scalar transfer functions from the disturbance to a given inter-storey drift can be represented as complex iterative maps. Using these expressions, two graphical approaches are proposed: one gives a method to achieve a prescribed value for the uniform boundedness of these transfer functions independent of the length of the mass chain, and the other is for a fixed length of the mass chain. A case study is presented to demonstrate the effectiveness of the proposed techniques using a 10-storey building model. The disturbance suppression performance of the designed interconnection is also verified for a 10-storey building model which has a different stiffness distribution but with the same undamped first natural frequency as the homogeneous model.