Response of seismic isolated structures with supplemental rotational inertia

Abstract

Motivated by the effectiveness of inerters to control the displacements of flexible structures in association with their known property to eliminate the participation of higher modes, this paper revisits the seismic response analysis of the classical two-degree-of-freedom isolated structure with supplemental rotational inertia in its isolation system. The paper shows that for the "critical" amount of rotational inertia which eliminates the participation of the second mode, the effect of this elimination is marginal on the structural response since the participation of the second mode is invariably small even when isolation systems without inerters are used. Our study, upon showing that the reaction force at the support of the inerter is appreciable, proceeds with a non-linear response analysis that implements a state-space formulation which accounts for the bilinear behavior of practical isolation system (single concave sliding bearings or lead-rubber bearings) in association with the compliance of the support of the inerter. Our study concludes that supplemental rotational inertia aggravates the displacement and acceleration response of the superstructure and as a result, for larger isolation periods (𝑇 𝑏 > 2.5 s) the use of inerters in isolation systems is not recommended.

Response Modification of Structures with Supplemental Rotational Inertia

“…While a driving spinning top, as the one shown in Figure 1.1 which is a physical realization of the inerter, has been familiar to several generations; inerters were apparently first proposed for the response modification of buildings in the mid-1980s by Kawamata (1986) and subsequently by Ishimaru (1994) and Arakaki et al (1999a,b) in the mid to late 1990s in Japan. Chen et al 2009;Kuznetsov et al 2011) who established, within the context of linear networks, the analogy of the inerter to the electric capacitor; a growing number of publications have proposed the use of inerters for the response modification of buildings by installing them at all floor levels (Furuhashi and Ishimaru 2008;Ikago et al 2012a,b;Takewaki et al 2012); at selected levels (Sugimura et al 2012;Ogino and Sumiyama 2014;Lazar et al 2014;Marian and Giaralis 2014;Taflanidis et al 2019) or at the ground level, either within the context of protecting a first soft-story (Makris and Kampas 2016;Makris and Moghimi 2019;Moghimi and Makris 2021), or within the context of enhancing a seismic isolation system (Saitoh 2007(Saitoh , 2012De Domenico and Ricciardi 2018b;Ye et al 2019;Makris and Moghimi 2022).…”