Summary In seismic base isolation, most of the earthquake‐induced displacement demand is concentrated at the isolation level, thereby the base‐isolation system undergoes large displacements. In an attempt to reduce such displacement demand, this paper proposes an enhanced base‐isolation system incorporating the inerter, a 2‐terminal flywheel device whose generated force is proportional to the relative acceleration between its terminals. The inerter acts as an additional, apparent mass that can be even 200 times higher than its physical mass. When the inerter is installed in series with spring and damper elements, a lower‐mass and more effective alternative to the traditional tuned mass damper (TMD) is obtained, ie, the TMD inerter (TMDI), wherein the device inertance plays the role of the TMD mass. By attaching a TMDI to the isolation floor, it is demonstrated that the displacement demand of base‐isolated structures can be significantly reduced. Due to the stochastic nature of earthquake ground motions, optimal parameters of the TMDI are found based on a probabilistic framework. Different optimization procedures are scrutinized. The effectiveness of the optimal TMDI parameters is assessed via time history analyses of base‐isolated multistory buildings under several earthquake excitations; a sensitivity analysis is also performed. The enhanced base‐isolation system equipped with optimal TMDI attains an excellent level of vibration reduction as compared to the conventional base‐isolation scheme, in terms not only of displacement demand of the base‐isolation system but also of response of the isolated superstructure (eg, base shear and interstory drifts); moreover, the proposed vibration control strategy does not imply excessive stroke of the TMDI.

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Summary The tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass‐amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base‐isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc‐Wen hysteretic model, representative of friction pendulum and of lead‐rubber‐bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai‐Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy‐based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well‐known shortcomings of TMD‐like systems. This important feature makes the TMDI particularly suitable for nonlinear base‐isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.

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The dynamic performance of base-isolated buildings can be improved by introducing a tuned mass damper (TMD) at basement, below the isolation floor where most of the earthquake-induced displacement demand is concentrated. In order to enhance the effectiveness of the TMD without simultaneously amplifying the relevant mass ratio, the use of supplemental inertial mass dampers has been envisaged by the authors and other authors in earlier studies. These schemes exploit the mass-amplification effect of the inerter, a twoterminal device whose generated force is ideally proportional to the relative acceleration between its terminals. In this paper, we present a review along with a systematic comparative study of six different strategies proposed in the literature, each one featuring a specific combination of mass-spring-dashpot elements arranged in series or in parallel with an inerter for the displacement mitigation of base-isolated structures. Frequency-response functions of each model are derived in closed form. Optimal design is based on a common strategy, considering a white-noise random process as seismic input, by minimization of the displacement variance but with an eye also for the superstructure acceleration (associated with forces arising in the superstructure) and for the TMD stroke. Then, the seismic performance of the six systems is assessed considering an ensemble of 52 natural earthquake ground motions, by comparing several response indicators including TMD stroke, deformation of the baseisolation floor, superstructure acceleration, interstory drifts, base shear, and reactions associated with spring, oil damper, and inertial damper supporting the TMD, which are significant for outlining preliminary economic assessments.