The impact of the frequency content of far-field earthquakes on the optimum parameters and performance of tuned mass damper inerter

Abstract

Tuned mass damper inerter is a passive control device that is proven to be effective in mitigating structural responses under earthquake excitations, however, its efficiency highly depends on its design parameters. This paper aims to investigate how the optimum parameters of TMDI change with the frequency content of far-field earthquakes to minimize the need for repeatedly optimizing these parameters for varying far-field earthquakes and structural characteristics. To achieve this objective, the ratio of the earthquake's frequency to the structure's frequency is defined as an index to simultaneously represent the structure and the earthquake. Case studies of 5, 10, 15, and 20-story building structures are analyzed under twenty-three far-field earthquakes which are categorized into three main groups based on their frequency (PGA/PGV) including “Low”, “Intermediate”, and “High”. Particle Swarm Optimization (PSO) is employed to obtain the optimum parameters of TMDI including the damping and the frequency ratio to minimize two distinct objective functions: (1) the peak displacement and (2) the peak acceleration of the top story in a time domain analysis. To validate the applicability of the proposed method in determining the optimal parameters of TMDI regardless of the earthquake and structure frequency, a 10-story benchmark building is employed. Moreover, this study demonstrates the effectiveness of TMDI in minimizing the objective functions concerning the frequency content of the earthquake. It also illustrates the trend of the PSO optimization process. The results show that the index provides a discernible pattern for the variation of the optimum parameters of TMDI. Furthermore, it is demonstrated that the difference in the structural response between tuning the TMDI with the PSO algorithm and the suggested method is less than 3 % when the index is greater than 1. As the ratio of earthquake frequency to the frequency of structure increases, the objective functions will correspondingly increase. The results also indicate that, an increment in the inertance ratio leads to an increase in the value of optimum parameters of TMDI. Furthermore, among all structures analyzed, those subjected to intermediate frequency earthquakes exhibit the most significant reduction in both objective functions.