Analysis of Structural Response Reduction to Earthquakes Using a Tuned Mass Damper Inerter (TMDI) System

Abstract

An inerter is a two-terminal mechanical element capable of generating a force proportional to the relative acceleration between its terminals, thereby enhancing the inertial effect in structural systems. The integration of an inerter with a Tuned Mass Damper (TMD) forms a Tuned Mass Damper Inerter (TMDI) system, which has the potential to improve vibration control performance under seismic excitation. This study aims to evaluate the effect of implementing TMDI on the dynamic response of building structures. The optimal design parameters of the TMDI were determined numerically by varying the frequency ratio (f) and damping ratio (ξ) based on the minimization of structural displacement response. The structural model analyzed in this study is a 12-story building equipped with a TMDI connected between the top floor and several lower floors. The analysis was conducted using a 12-story MDOF model based on MATLAB, with parameter optimization performed using the fminimax function and time-history evaluation under several earthquake records. The results show that connecting the TMDI to at least the 6th floor can reduce the structural responses in terms of displacement, acceleration, and velocity by approximately 50%, 41%, and 36%, respectively, compared with the structure without an inerter. In addition to providing greater response reduction, the TMDI system requires a smaller additional mass compared with a conventional TMD. To achieve approximately 20% response reduction, the TMDI requires a mass that is about four times smaller than that required by a TMD.