Filter-based inerter location dependence analysis approach of Tuned mass damper inerter (TMDI) and optimal design

Tuned Mass Damper Inerter (TMDI) is a novel type of dynamic vibration absorber for achieving lightweight design while maintaining excellent control performance. Compared to traditional Tuned Mass Damper (TMD), the complex dependence characteristics of inerter bring difficulties to evaluate the control performance and design the inerter. In order to address this problem, this paper investigates the vibration control of TMDI subjected to wind and seismic loads. The closed-form solutions of the control performance of TMDI are obtained via a filter approach. By using the filter approach, the computation cost is largely reduced in calculating structural responses and control performance. Subsequently, the empirical formulas for determining optimal design parameters (frequency ratio νopt and damping ratio ζdopt) based on mass ratio μ, inertance ratio β and inerter location parameter φ is proposed. By comparing the optimal control performance of TMDI with TMD, the inerter dependence analysis is conducted to investigate the enhancement effect. An index β·(1–φ)2/μ is proposed as a criterion, where β·(1–φ)2/μ ≥ 1 indicates that the control performance of TMDI is enhanced by inerter. In addition, TMDI results in similar performance to TMD with an equivalent mass ratio μe = μ + β·(1–φ)2. Based on the investigation of an actual high-rise chimney, the proposed formulations and criterion are validated. The wind- and seismic-induced responses are reduced up to 60% and 55% respectively. The proposed method provides guidance for determining the optimal parameters of TMDIs.