Optimal design of the ideal grounded tuned mass damper inerter for comfort performances improvement in footbridges with practical implementation considerations

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.