Pareto Optimal Design of the Tuned Mass Damper

Ahmed Abed,Om El Khaiat Moustachi

doi:10.13189/cea.2022.100120

Abstract

Strong vibrations due to wind induced loads and earthquakes have undesirable effects on tall buildings and long-span bridges, and can cause discomfort, dizziness and anxiety for their occupants and users. The Single Tuned Mass Damper (STMD) is vibration control device used to mitigate strong motion. This study investigated the STMD from the perspective of multi-objective optimization. The main goal was to identify and characterize the Pareto set of optimal STMD parameters in terms of damping and stiffness. The optimization was performed using a multi-objective optimization algorithm based on gradient descent and successive bisecting of the search domain. <img src=image/14825382_01.gif> and <img src=image/14825382_02.gif> norms of the transfer matrices for structural displacement and acceleration were considered as design objectives. We found that for peak response reduction, irrespective of the excitation type, structural damping and STMD mass ratio, the Pareto set was linear and extended mainly in the direction of frequency ratio, while the damping ratio varied marginally within the set. For RMS displacement and peak acceleration minimization, the Pareto set was composed of two segments. Additionally, in all instances, the Pareto set was found to be bounded by the single-objective optimal STMDs for the considered design objectives. The implications of the findings were discussed and approximations of the Pareto optimal STMD were suggested.

Highlights

Vibration control has become a requirement for the design of secure and reliable tall buildings and long-span bridges
The main goal of this study was to investigate the behavior of the Pareto optimal Single Tuned Mass Damper (STMD), and characterize the Pareto set of optimal designs for structural vibration mitigation
The slope of the Pareto front was −0.827, which indicated that the considered design objectives were competing objectives, and the reduction in peak displacement was higher than the reduction of peak acceleration across the Pareto set (Fig. 3B)

Summary

Introduction

Vibration control has become a requirement for the design of secure and reliable tall buildings and long-span bridges. With the advancement of construction materials and methods, the stiffness of tall and long structures has declined. Structures became more prone to dynamic effects caused by earthquakes and wind induced loads. Strong vibrations threatened the structural integrity of buildings and bridges, and the comfort of users and occupants [1]. In this regard, vibration control is considered one of the costeffective solutions to mitigate such problems. A wide range of control strategies and devices were researched and developed during the last century [2], and the Single Tuned Mass Damper (STMD) is one of the most well known and mature [3]

Objectives

Methods

Results

Conclusion