Analytical Solution of Seismic Responses of Multi-Storey Building Structures Controlled by Tuned Mass-Damper-Inerter (TMDI)

Ayman Abd-Elhamed1,2,Email

Soliman Alkhatib3

1Physics and Engineering Mathematics Department, Faculty of Engineering-Mattaria, Helwan University, Cairo 4034572, Egypt.

2Faculty of Engineering, King Salman International University, South Sinai, El‑Tur, Egypt.

3Engineering Mathematics and Physics Department, Future University in Egypt, Cairo 11835, Egypt.

Abstract

The tuned mass-damper-inerter (TMDI) is a newly developed passive energy dissipation unit that combines the conventional tuned mass-damper (TMD) with an inerter mechanism to attenuate undesirable vibrations. This study provides a comprehensive evaluation of the impact of TMDI on the structural response of linear-behaving multi-degree-of-freedom (MDOF) structures subjected to far- and near-fault earthquake-induced ground shaking. The chosen near-fault records guarantee motions with forward directivity (FD) and motions with fling step (FS). An approach based on a genetic algorithm (GA) is used to tackle the optimization problem. The controlled response's objective function is focused on two key factors that are studied separately: minimization of inter-story drifts and minimizing of horizontal peak floor acceleration. It is analytically demonstrated that the TMDI performs better than the conventional TMD for relatively small mass ratios, regardless of the distance from a fault rupture. However, the TMD's high-mode dampening effect can be further enhanced by increasing the inertance of the inerter. Additionally, buildings excited by near-fault records with FS have a higher seismic demand on their induced responses. Lastly, the inerter's mass-amplification effect can either enhance the performance of the conventional TMD, for a certain TMD mass, or replace a portion of the TMD's oscillating mass, to realize a substantial weight reduction at a desired level of vibration suppression.

Analytical Solution of Seismic Responses of Multi-Storey Building Structures Controlled by Tuned Mass-Damper-Inerter (TMDI)