Optimum tuning frequency and damping ratios in Inter-story Isolation Systems (non-conventional TMDs): a closed form solution

The Inter-story Isolation System (IIS) is a passive strategy in the field of structural vibration control deriving from the Base Isolation System (BIS). The IIS is realized shifting the position of the isolation layer upward, from the base of the building to an intermediate level, thus sub-dividing the structure in two portions, namely the lower structure and the isolated upper structure.From a dynamic point of view the isolated upper structure behaves as a Tuned Mass Damper (TMD) for the lower structure. Therefore, unlike conventional TMD, in IIS the device mass is comparable to the main mass, combining control and structural functions.This paper proposes an optimization procedure for inter-story isolation structures for deriving in closed form the optimum tuning frequency between isolated upper structure and lower structure, and the optimum damping ratio of the isolation system. In particular, this procedure represents an extension of the “fixed-points” theory of Den Hartog for damped structure –damped TMD with large mass ratio. The authors formulate an analytical approach by adopting a simplified two degree-of-freedom model for calculating the optimum parameters of inter-story isolation systems, i.e. the tuning frequency and the damping ratios,that minimize the displacement amplitude of the lower structure under harmonic excitation. In addition, the influence of the damping in the lower structure is investigated. Finally the optimization process is validated by comparing the results of frequency response analyses obtained by adopting the proposed optimum expressions and the main optimum formulae provided in literature.