Advanced computational design of shared tuned mass-inerter dampers for vibration control of adjacent multi-story structures ⋆ F. Palacios-Qui˜ nonero ∗ J. Rubi´ o-Masseg´ u ∗ J.M. Rossell ∗ H.R. Karimi ∗∗ ∗ Department of Mathematics, Universitat Polit` ecnica de Catalunya, Av.Bases de Manresa 61–73, 08242 Manresa, Barcelona, Spain (e-mail: {francisco.palacios, josep.rubio, josep.maria.rossell}@upc.edu). ∗∗ Politecnico di Milano, Department of Mechanical Engineering, via La Masa 1, 20156 Milan, Italy (e-mail: hamidreza.karimi@polimi.it) Abstract: Inerters are a novel type of mechanical actuation devices that are able to produce large inertial forces with a relatively small mass. Due to this property, inerters can provide an effective solution to the main drawbacks of tuned mass-dampers and, consequently, they are gaining an increasing relevance in the field of passive structural vibration control. In this paper, a computational design strategy for inerter-based vibration control schemes is presented. The proposed approach combines a computationally effective reduced-frequency H ∞ cost-function and a constrained global optimization solver to design different configurations of a shared tuned mass-inerter-damper system for the seismic protection of a multi-story two-building structure. To assess the effectiveness of the obtained configurations, the frequency characteristics and the seismic response of the interstory drifts and interbuilding approaches are investigated with positive results. Keywords: inerters, structural vibration control, multi-structure systems, genetic algorithms, shared tuned mass-damper 1. INTRODUCTION Protection of large buildings and civil structures against the damaging effects of external natural disturbances, such as wind gusts, earthquakes, or ocean waves is a research area of significant theoretical and technical interest. In the past few decades, a large number of active, passive and semi-active structural vibration control strategies has been proposed and, some of them, implemented in practice with positive results [Spencer and Nagarajaiah (2003); Ikeda (2009); Li and Huo (2010); Rubi´ o-Masseg´ u et al. (2012); Bakka and Karimi (2013)]. Passive vibration control sys- tems (PVCS) are simple and robust, and do not require power supply. A good example of PVCS is the tuned mass- damper (TMD), which consists in a proper combination of elastic, damping and mass elements that are attached to the main structure to absorb and dissipate its vibrational energy. In order to provide a good level of vibrational mitigation, the TMD strategy requires the attached mass to be as large as possible. In the case of large structures, this fact makes the TMD a huge and massive device whose accommodation poses serious structural problems [Giaralis and Taflanidis (2016)]. Inerters are a new kind of passive elements in mechani- cal systems that are attracting increasing research atten- tion in recent years. The ideal inerter is a massless two- terminal device that produces a resistant force of the form ⋆ Partially supported by the Spanish Ministry of Economy and Competitiveness under Grant DPI2015-64170-R/FEDER. F (t)= b ( ¨ x 2 (t) − ¨ x 1 (t) ) , where ¨ x 1 (t) and ¨ x 2 (t) represent the inerter terminals’ acceleration and b is a constant called inertance. A key feature of the actual inerter is that its inertance can be two or more orders of magni- tude higher than its mass. As a consequence, light and compact devices that are able to develop large inertial forces can be seriously considered in practical applications [Smith (2002)]. This fact, and the two-terminal character of the inerter elements, naturally leads to explore new passive vibration control schemes, such as inerter-based multi-element distributed systems and more sophisticated spring-damper-inerter layouts [Chen et al. (2013); Lazar et al. (2014); Marian and Giaralis (2014)]. In this context, obtaining efficient tools to compute suitable values for the inertance, stiffness and damping coefficients appears as a central issue. The objective of the present work is twofold: (i) to provide a proper computational design methodology for the new inerter-based vibration control schemes, and (ii) to demon- strate its effectiveness in a structural vibration control problem of moderate complexity and dimension. To meet the first goal, we have introduced an appropriate cost function J (θ), which is based on the discrete approxima- tion of a restricted frequency-range H ∞ norm. This cost function provides a fast and meaningful evaluation of the vibrational cost associated to the parameter configuration θ, and makes it possible to obtain an optimal parameter configuration ˆ θ by using standard tools for constrained global optimization. To address the second objective, the Preprints of the 20th World Congress The International Federation of Automatic Control Toulouse, France, July 9-14, 2017 Copyright by the International Federation of Automatic Control (IFAC) 13908