Analytical optimal design and performance evaluation of series tuned inerter damper for ground motion excited structures

The series tuned inerter dampers (STID) with distributed inerters are proposed in this paper to suppress seismic response for ground motion excited structures with broadband characteristics. In order to reveal the mechanism of the STID for vibration mitigation, the dimensionless displacement objective function of a single degree of freedom structure equipped with an STID under random Gaussian white noise base excitations is thereupon derived. Based on the principle of the reasonable distribution of inertance, the analytical optimal design parameters of STID are obtained under constraint for total inerter-mass ratio. The vibration mitigation performance of the STID is evaluated and further compared with the tuned inerter damper (TID), tuned mass damper (TMD) and typical series dampers using same mass ratio or inerter-mass ratio when structure is subjected to harmonic and random excitation. Results demonstrate that the performance of structural vibration control and broadband characteristics of STID outperform both the TMD and TID. On the condition of same inerter-mass ratio, the deformation enhancement of damping element can be further increased compared with TID because of dual-tuning effect of series inerters. The higher vibration control performance of STID is realized by using very small nominal damping ratio compared with the TMD and TID. Meanwhile, there exist two grounded inerters in STID compared to other series dampers, and both two subsystems are not affected by base random acceleration excitation which also brings STID a wider VSB and better seismic response mitigation effect. Substantially, due to STID is a type of dual-grounded inerter-based device, for force and base acceleration excited main system, the optimal expressions are identical. Hence, STID can adapt to more complex practical engineering and random and diverse excitations. Hence, the STID can be deemed to be a broadband, high effectiveness and high-performance inerter system. Meanwhile, considering low damping, lightweight and flexible install of STID, it is easier for implementation in practical engineering.