Design Spectra for Intermediate Isolation Systems: Closed-Form Relationship Based on Application of Pole Allocation Method

In this paper, closed-form expressions are derived for tracing some displacement spectra to be used for the preliminary design of Intermediate Isolation System (IIS), with specific reference to the case of IIS obtained through isolated vertical extension of existing buildings. The so-called Intermediate Isolation System (IIS) design spectrum provides the drift in the lower structure varying the isolation period, thus allowing for identifying the design solution that maximizes the mass damping effect on the lower structure. The IIS design spectrum is derived by means the pole allocation method applied to two-degree-of-freedom model. Indeed, using the pole allocation method, it is possible to obtain the value of the modal damping ratios in closed form for non-classically damped systems, such as IIS. Known such modal damping ratios, it is possible to apply the CQC modal superposition method in response spectrum analysis, thus obtaining the IIS design spectrum. Similarly, it is possible to obtain the isolators displacement spectrum, to determine the design displacement of the isolation devices, which implicitly considers both the mass damping effect and the flexibility of the lower structure. Finally, the lower structure and isolator responses derived from these design spectra for IIS are compared with the ones obtained from linear time history analyses.