## 1 Introduction
[PERSON] and [PERSON] (2023) developed a Semi-Active Bypass Fluid Damper (SABFD) for bridge vibration control, employing programmable logic controllers (PLCs) and fuzzy control algorithms [22]. This innovation significantly reduced bridge displacements and improved structural responses under traffic-induced vibrations. [PERSON] et al. (2024) introduced a rubber bracing damper (RBD) system using high-damping rubber to dissipate energy, which was shown to reduce lateral displacements and prevent the formation of plastic hinges, enhancing seismic performance by up to 69% [23]. The advancements in damper technology reflect a growing interest in developing systems capable of effectively managing seismic loads driven by the increasing frequency of earthquakes and other natural hazards [24]. Different types of dampers, such as Tuned Mass Dampers (TMDs), tuned liquid dampers (TLDs), and Tuned Liquid Column Dampers (TLCDs), have been explored for maintaining and retrofitting structures [25]. As these studies indicate, the evolution and refinement of damper systems continue to play a vital role in safeguarding structures against seismic forces and improving overall resilience. Viscous dampers (VDs) are a form of base isolation commonly used to dissipate energy and enhance the damping ratio of structures, ensuring their stability and safety. [PERSON] and [PERSON] (2012) noted that examples of liquid dampers include tuned liquid dampers (TLDs) and Tuned Liquid Column Dampers (TLCDs). In contrast, VDs are a type of Dynamic Vibration Absorber (DVA) that is simple and easy to manage [26]. Viscous dampers are particularly beneficial for buildings due to their low maintenance requirements and cost-effectiveness [25], as well as their practical application. The rapid advancement of damper technology highlights the significant impact these devices have in addressing issues related to the strength and stability of buildings. VDs are utilized in various applications, including vehicle suspensions, high-rise buildings, bridge supports, and machinery suspensions. According to [PERSON] et al. (2015), VDs can dissipate energy in buildings at different levels of vibration while simultaneously maintaining stiffness. Buildings and structures that endure disasters typically require repair and retrofitting. VDs are a preferred option for such strengthening and retrofitting work due to their compact size and ease of installation [27]. [PERSON] et al. (2024) investigated the open-space viscous damper installation configuration (OSVDIC) that balances structural and architectural needs. Their shaking table tests on a three-story steel-frame model showed that OSVDIC significantly reduced seismic responses and effectively dissipated energy during earthquakes. The study confirmed the model's accuracy and highlighted OSVDIC's potential to meet damping requirements while addressing aesthetic and functional considerations [28]. Installing viscous dampers (VDs) is challenging in terms of space and area since these components are longitudinal and not applicable for limited space, particularly in existing buildings. However, VDs have the advantage of dissipating loads from multiple directions, making them effective in various seismic scenarios. The movement of structures is influenced by the loads applied, and ground motion due to seismic activity provides a good example of this. When a building experiences ground movement, it may eventually reach a point where its displacement exceeds the design limitations, causing the structure to show signs of weakness and fatigue. At this stage, the building may be at risk of collapse. Structural failures can be attributed to several factors, including earthquakes, design limitations, and defects or damage to elements due to building vibration [29]. Therefore, the type and amount of load that a building may encounter should be carefully considered during the design phase to prevent collapse. Recent designs of VDs have been optimized for installation in constrained spaces.