# Effect of Dynamic Loading Conditions on Maximizing Energy Dissipation of Metallic Dampers
## 1 Introduction  
Beyond simply increasing the stiffness of structures for seismic reinforcements, modern designs withstand earthquakes by installing additional dampers. Among the various dampers, hysteretic dampers have relatively low cost, excellent durability, and high reliability because of their sustainable nature, as they use the plasticity of materials [1, 2]. Hysteretic dampers, such as steel shear dampers or unbounded braces, dissipate seismic energy through the plastic deformation of materials, which are generally metals. The metallic dampers can be applied to retrofit buildings with a relatively small scale of deformation [3, 4]. In addition, based on their ease of installation, they can potentially be applied to structures under various conditions, such as transmission lines or overhead contact systems [5, 6]. Accordingly, many researchers have proposed novel concepts of metallic dampers using assorted approaches, such as a crawler steel damper [7], steel plates with a vertical free mechanism [8], a hysteretic damper with torsional yielding [9], rippled of metallic plate dampers [10, 11], and a steel tube-in-tube damper [12]. Moreover, the efficiencies of existing metallic dampers have also been improved to facilitate installation in large-scale structures. For example, shape-optimization studies for a shear slip damper [13], a steel shear panel damper (SSPD) [14], a U-shaped damper [1], and a coupling beam metal damper [15] have been conducted. However, none of these studies developed or evaluated their dampers with respect to different capacity requirements under various installationconditions. Furthermore, the conventional studies optimize dampers by increasing the energy dissipation capacity and stiffness, mostly depending on static experiments or analysis. Therefore, sometimes statically optimized dampers might not perform as expected under real earthquakes, which are dynamic, especially when the earthquakes are relatively small.  
In this context, this study aims to develop a progressive development process for metallic dampers with a simple hypothetical installation concept. This process is based on the methodology of shape optimization under dynamic loading conditions. Most studies on the optimized shape of metallic dampers have focused on flexural yielding; that is, in-plane bending. In our study, with the same notion of flexural yielding, the simplest concept of a metallic damper is presented. However, unlike static optimization studies that have been conducted several times in the past, this study presents a new methodology of dynamic optimization of metallic dampers. Based on this concept, this study suggests various approaches to optimize the geometry of the damper.  
As metallic dampers can be manufactured in various shapes, this study focuses on developing specialized shapes for different target capacities. Several diverse conditions were applied to establish the distinctive optimization methodology of this study in order to derive a variety of shapes optimized for different conditions. Through alteration of the optimization conditions, the effects of the maximum stroke size, the number of loading cycles, and the presence of additional control variables were studied. Consequently, a novel approach was constructed with the application of a simple model for the optimization process, including dynamic analysis. The overall development process was conducted via an optimization algorithm combined with the finite element (FE) software ABAQUS 6.14. This calculation process maximized the energy dissipation capability of the damper; as a result, the optimal shapes were derived.