Tuned mass dampers (TMDs) are typically introduced and calibrated as natural passive control devices for the vibration mitigation of the steady-state response of primary structures subjected to persistent excitations. Otherwise, this work investigates the optimum tuning of TMDs toward minimizing the transient structural response. Specifically, a single-degree-of-freedom (SDOF) system is considered as a primary structure, with added TMD, subjected to pulse-like excitations. First, the system is analytically analyzed, within the time domain, for unit impulse base displacement, through Laplace transform. Then, the tuning process is numerically explored by an optimization procedure focused on an average response index, to extract the optimum condition toward best TMD calibration. The efficiency of the proposed control device is then assessed and demonstrated through further post-tuning numerical tests, by considering as dynamic loadings: first, a time unit impulse base displacement, coherent with the source description above; second, different pulse-like excitations, to detect the effectiveness of the so-conceived TMD for generic ideal shock actions; third, a set of nonstationary earthquake excitations, to enquire the achievable level of seismic isolation. It is shown that this leads to a consistent passive TMD in such a transient excitation context, apt to mitigate the average response. Additionally, the present tuning forms a necessary optimum background for a possible upgrade to a hybrid TMD, with the potential addition of an active controller to the so-optimized TMD, to achieve even further control performance, once turned on, specifically for abating the peak response, too.

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