Preserving cultural heritage against earthquake and ambient vibrations can be an attractive topic in the field of vibration control. This paper proposes a passive vibration isolator methodology based on inerters for improving the performance of the isolation system of the famous statue of Michelangelo Buonarroti Pietà Rondanini. More specifically, a five-degree-of-freedom (5DOF) model of the statue and the anti-seismic and anti-vibration base is presented and experimentally validated. The parameters of this model are tuned according to the experimental tests performed on the assembly of the isolator and the structure. Then, the developed model is used to investigate the impact of actuation devices such as tuned mass-damper (TMD) and tuned mass-damper-inerter (TMDI) in vibration reduction of the structure. The effect of implementation of TMDI on the 5DOF model is shown based on physical limitations of the system parameters. Simulation results are provided to illustrate effectiveness of the passive element of TMDI in reduction of the vibration transmitted to the statue in vertical direction. Moreover, the optimal design parameters of the passive system such as frequency and damping coefficient will be calculated using two different performance indexes. The obtained optimal parameters have been evaluated by using two different optimization algorithms: the sequential quadratic programming method and the Firefly algorithm. The results prove significant reduction in the transmitted vibration to the structure in the presence of the proposed tuned TMDI, without imposing a large amount of mass or modification to the structure of the isolator.
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