A novel tuned mass damper inerter: optimal design, effectiveness comparison, and robustness investigation

Abstract

This study proposes a novel tuned mass damper inerter (NTMDI) by altering the position of the damping element in tuned mass damper inerter (TMDI) or adding an inerter element to a variant tuned mass damper (VTMD). The proposed NTMDI can be regarded as a more general case of tuned viscous mass damper. A detailed mechanical model for a single-degree-of-freedom (SDOF) structure with NTMDI is introduced, and the optimal design of NTMDI is derived theoretically based on fixed-point theory. Analytical solutions for NTMDI optimal design, including the optimal frequency ratio and damping ratio, as well as the optimal dynamic amplification factor of the structure, are obtained. Then, considering three types of loads: including harmonic excitation, white noise excitation and natural seismic excitation, the effectiveness of NTMDI for vibration control was evaluated by comparing it with three other classical tuned mass dampers (TMD, VTMD, and TMDI). The results demonstrate that adding inertance to TMD and VTMD can significantly improve their effectiveness in mitigating structural responses. Additionally, it is found that NTMDI is more efficient in reducing structural responses than TMDI and the frequency range controlled by NTMDI is wider than that controlled by TMDI when the tuned physical mass and inertance of NTMDI are identical to those of TMDI. Finally, a series of robustness investigations are carried out, and NTMDI exhibits superior robustness to TMDI in situations where positive tuning occurs in the optimal frequency ratio. However, in cases where negative tuning is present, TMDI outperforms NTMDI. Fortunately, TMD, VTMD, TMDI, and NTMDI demonstrate excellent robustness in terms of damping.