# Intermediate Isolation System with Nonlinear Lower Structure and Isolation System
## 1 Introduction  
The Intermediate Isolation System (IIS) derives from the Base Isolation System (BIS) by shifting the position of the isolation layer upward. Therefore, a building can be ideally subdivided into a sub-structure and super-structure, respectively placed below and above the isolation interface. Due to the flexibility of the lower structure, the dynamic behaviour of the IIS is more complex and less intuitive than that of the BIS. The IIS is characterized by a twofold dynamic behaviour that combines two strategies of passive control: the isolation of the upper structure and mass damping on the lower structure. In particular, the isolated upper structure behaves as a base isolated structure on the roof of the lower structure and, at the same time, as a mass damper for the lower structure. Unlike conventional tuned mass dampers (TMD), in which the mass of the absorber is an added mass of only few per cent of the structural mass, in the IIS a part of the building is converted into a mass damper, with a mass that can be comparable to, or even larger than, the mass of the lower structure. For this reason, the IIS is also termed as _non-conventional mass damper, building mass damper_, or _inhibited mass damper_. By increasing the mass of the TMD, the robustness of the system increases; consequently, the seismic response is less sensitive to variations of the design parameters, and to the frequency content and impulsive character of the seismic input [1]. By exploiting this robustness, some actual IIS buildings have been designed in Japan as \"untuned\" mass dampers [2; 3; 4]. In Japan the IIS is quite diffused and has gained significant popularity, so that more than 60 buildings have been realized in the past 20 years [5]. This system is frequentlyused for new construction buildings, in particular tall buildings. Some examples are the Iidiabashi 1 st Building, Shiodome Sumitomo Building, Nakanoshima Festival Tower, Tekko Building, and Roppongi Ground Tower [2,3,6,7,8,9,10]. Only in a few cases has the IIS has been adopted for expanding vertically existing buildings, as in Berry St. in San Francisco, USA [11,12], and the Musashino City Disaster Prevention and Safety Centre in Tokyo, Japan [2,3]. In the last decade, several researchers have studied IIS in order to understand its dynamic behaviour, identify the governing mechanical parameters, and derive design indications that ensure good seismic performance. Important contributions, of course, come from Japan; in particular, some researchers [2,3,6,7] deal with the IIS as a \"concentrated energy dissipation\" design problem, considering that most of the seismic energy input is absorbed by isolator and damper devices installed in the isolation layer. Other Japanese researchers [13,14,15] adopt two-degrees-of-freedom (2 DOF) models and have proposed a seismic response prediction method in which the natural mode functions are incorporated into the energy-balance method, firstly suggested by [PERSON] [16], to derive the seismic response of the system. Additional contributions are given in [17,18,19], where the impact of the dynamic interaction between upper and lower structures and the effect of the possible coupling of the higher modes are investigated by adopting simplified three-degree-of-freedom (3 DOF) models; the results of the analyses are also compared to the outcomes of experimental campaigns [20,21]. In other papers [22,23], an optimization procedure is proposed using 3 DOF models to enhance the seismic performance of both upper and lower structures. [PERSON] [24] has recently suggested the pole allocation method applied to 3 DOF models for analysing the dynamic characteristics of intermediate isolation systems and elaborating a mathematical solution in closed form. In a subsequent paper [25], the method has been generalized for including any passive control strategy (base isolation, inter-story isolation, tuned mass dampers, viscous dampers). [PERSON] et al.