In recent years, inerter vibration absorbers (IVAs), such as the tuned mass damper inerter (TMDI), attracted much attention in the literature for reducing seismic displacement demands of base isolated structures (BISs). Several theoretical studies reported reduced BIS seismic demands with increasing inertance endowed by a grounded inerter element, but adopted mostly idealized linear dynamical models. Herein, the potential of TMDI‐configured IVAs for seismic response reduction of BISs modelled as single‐mass structures is assessed under the combined effects of nonlinear inerter and structural behavior. To this aim, experimental data from a shaking table testing campaign are considered utilizing a custom‐built flywheel rack‐and‐pinion grounded inerter prototype with variable inertance, along with high damping rubber bearings in the isolation layer and in the BIS‐to‐absorber link. White noise excitation and an ensemble of six ground motions (GMs) with different frequency content are used in the tests for which bearings exhibit softening nonlinear behavior. Experimental results demonstrate improvement of BIS nonlinear seismic response in terms of displacement and base shear with increasing inertance for nonlinear and nonoptimally tuned IVAs. It is found though that the considered IVAs may be detrimental to BIS acceleration response depending on the GMs time‐varying frequency content signatures as captured by the continuous wavelet transform spectrogram. Finally, it is concluded that representing the inerter device by a simplified linear dissipative model as opposed to a nonlinear model with friction and gear backlash suffices to trace the BIS response with acceptable accuracy and, thus, can be used for optimal seismic TMDI design.

The paper focuses on the optimal design of the grounded tuned mass damper inerter (TMDI) in footbridges and on some practical implementation issues. An optimal design procedure is implemented for the perfectly grounded ideal TMDI (infinite stiffness of the connection at the ground plus linear and nondissipative inerter). The procedure is based on reduced-order models of the footbridge by assuming the frequency ratio and damping factor as design parameters, for a given number of values of the TMDI the inertance and mass ratios aiming at minimizing the maximum acceleration response of the system for users' comfort improvement under performance criteria defined in Human-induced Vibration of Steel Structures (HiVoSS) guidelines. The procedure is applied to an existing footbridge suffering excessive human-induced vibrations. After the optimal design of the TMDI has been found, its performances are assessed by the avail of a fully 3D finite element model of the case-study footbridge, which has been calibrated toward an in situ experimental identification campaign. Alternative proposals for practical implementation of the control system are analyzed. Finally, a performance sensitivity analysis is carried out regarding the deviations from the initial assumption of perfectly grounded TMDI system, by varying the stiffness of the connection at the ground of the ideal inerter. Results show that the proposed procedure makes the TMDI a very efficient control system for footbridges and that changes of the stiffness of the grounded connection drop the beneficial effect of the TMDI, also if consequences of such errors are less than the ones occurring in classical TMDs for detuning or malfunctioning.

In this paper we study the semi-active control of structural systems by means of variable stiffness devices, and the resulting non-linear dynamics of the controlled system. In particular, the study is applied to base-excited single-degree-of-freedom systems, controlled by variable ON–OFF elastic devices and subjected to simple motion conditions: free vibrations following initial conditions and stationary response to harmonic input. A performance index, which, in the case of base-excited structures, assumes an original dual formulation following the relative or absolute approaches, has been proposed for instantaneous optimal control. The study includes both the optimal control design and the observation of the resulting non-linear dynamics of the controlled system. The dynamic behavior of the controlled non-linear system is studied with respect to the parameters which characterize the algorithms, the control device, and the input. In this way, also by means of significant (and original) analytical solutions of the equations of motion, the optimal formulation of the algorithms, some particular behaviors of the controlled systems, and the performances of the control approach are shown and explained for the different control strategies.