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The traditional aseismic design, for mitigating the damaging effects of earthquakes, depends on the energy dissipation by inelastic deformations of structural elements through the introduction of flexibility and/or energy absorption capability within the structural system itself. On the other hand, there are protective techniques which can limit or eliminate inelastic action to the structure, reduction of response as well as acceleration of superstructure, thereby protecting the structural as well as nonstructural elements. Extensive research works have been done in the area of passive vibration control to mitigate the vibration effect of structures (Housner et al, 1997; Marano et al, 2013). One of the protective techniques is base isolation (BI) system whereby it elongates the time period of the structure from the dominant frequencies range of ground motion which is detrimental for the structures and hence the superstructure is conceived with lesser amount of shear force transmitted through the base. Various BI devices, such as rubber bearings, lead rubber bearings (LRB), high-damping rubber bearings, friction pendulums, and resilient friction bearing isolators, are conventionally adopted for seismic protection of buildings and bridges.
The usefulness of BI systems and their performances have been extensively studied in the past (Buckle & Mayes, 1990; Jangid & Dutta, 1995; Spencer & Nagarajaiah, 2003; Symans & Constantinou, 1999). These studies provided insight into the behaviour of such systems. Experimental and analytical studies on the seismic response of isolated bridges by sliding isolation systems (Constantinou & Tadjbakhsh, 1985; Kartoum, Constantinou, & Reinhorn, 1992; Tsopelas, Constantinou, Kim, & Okamota, 1996a; Tsopelas, Constantinou, Okamota, Fujii, & Ozaki, 1996b) clearly indicate that such devices are quite effective. The BI bearings are installed between the bridge deck and pier to lengthen the period of the deck and therefore the time periods of the isolated deck are going away from the dominant periods of the earthquake ground motions. This effectively reduces the shear force transmitted through the pier as base shear at the pier occurs due to the deck mass alone (Jangid, 2004). The effective stiffness and damping of isolation bearings has been proposed (Hwang & Sheng 1994) for designing sliding system. A comprehensive review on rubber bearings and hysteretic dampers can be obtained from Kunde and Jangid (2003).
It is well established that the performance of BI system is largely dependent on the characteristics of the isolator parameters for best performance (Baratta & Corbi, 2004). The BI system optimization has been performed in the framework of random vibration analysis considering stochastic descriptions of earthquake events. The stochastic response of typical three-span bridge structure with seismic isolation system consisting of rubber bearings and hysteretic dissipaters using the equivalent linearization technique is studied by Li (1989), Pagnini and Solari (1999). Usually, a standard nonlinear optimization problem is formulated to minimize the stochastic response of the structure, referred as Stochastic Structural Optimization (SSO) (Taflanidis, Jeffrey & Beck, 2008). A major limitation of such deterministic approach is that the uncertainty in the performance-related decision variables cannot be included in the stochastic response analysis and the related optimization procedure. It has been demonstrated that the interplay among the parameter uncertainty and loading uncertainty (Jensen, 2005) can markedly change the response of a system and thereby the safety of structure (Chaudhuri & Chakraborty, 2006). The optimal design is also observed to be changed significantly by system uncertainty (Schuëller & Jensen, 2008). Many notable works have been done in the field of passive vibration control considering system parameter (Papadimitriou and Katafygiotis 1997, Taflanidis et al. 2008a, Marano & Quaranta, 2009; Lucchini, Greco, Marano & Monti, 2014; Greco, Marano & Fiore, 2016) but limited literatures are available in seismic vibration mitigation utilizing BI system considering uncertain parameters.