Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)

The paper concerns the optimal design and performance evaluation of a Tuned Mass Damper Inerter (TMDI) to reduce dynamic vibrations. The system exploits properties of the inerter, a two-terminal mechanical device able to produce a force proportional to the relative acceleration between terminals, with the ability of generating an apparent mass even two orders of magnitude greater than its own physical mass. A primary single-degree-of-freedom structure is equipped with a classical linear Tuned Mass Damper (TMD), the secondary structure, whose mass is connected to the ground via an inerter. The optimal design of the TMDI is conducted by assuming a white noise process as base input and utilizing three different design methodologies: displacement minimization, acceleration minimization and maximization of the ratio between the energy dissipated in the secondary system and the total input energy. Optimal results obtained with the different methodologies are carried out and compared. Two limit cases are also considered when the inerter is not contemplated: conventional and non-conventional TMDs, characterized by a low and a large mass ratio, respectively. The TMDI performance is evaluated and compared with conventional and nonconventional TMDs; moreover, its robustness is assessed with a sensitivity analysis varying the design parameters. Attention is focused not exclusively on the primary structure response but also on the secondary one. Finally, the effectiveness of the optimally designed TMDI is evaluated having considered earthquake base excitation. Results demonstrate the effectiveness of TMDI systems for dynamic response reduction with superior performances and robustness than classical TMDs.