## 1 Introduction  
In recent years, many different innovative types of damping systems have been developed, such as Sliding LRBs [1], superelastic pendulum isolators [2], and passive adaptive isolation bearings (PAIBs) [3] all manufactured by Southeast University in Nanjing, China, which demonstrate high performance in successfully dissipating applied vibrations in structures. However, these systems are applicable only in newly designed structures, and their practical use is not common. Additionally, these devices do not require much space for installation, but they are not suitable for areas with limited space. In recent years, significant strides have been made in the development of viscous damper technology and damping systems to enhance the safety and efficiency of structures under seismic conditions. Various techniques have been employed for the seismic retrofitting of buildings, with the installation of supplementary damper devices being one of the most effective methods. [PERSON], [PERSON], and [PERSON] (1999) emphasized the role of such dampers in dissipating structural vibrations, thereby enhancing the integrity and stability of buildings ([PERSON] and [PERSON], 2014). Consequently, numerous studies have explored the implementation of dampers to reduce displacement and increase seismic performance ([PERSON] and [PERSON], 2014). The exposure of structures to severe deformations due to external forces, like earthquakes, tsunamis, or strong winds, can cause substantial damage. [PERSON] and [PERSON] (2008) asserted that structural components often suffer damage due to the horizontal or rotational movement of buildings under such conditions ([PERSON] and [PERSON], 2014). [PERSON] et al. (2011) studied the vulnerability of multi-story reinforced-concrete buildings during earthquakes, particularly focusing on the effect of soft stories, where reduced lateral stiffness leads to structural failure. They found that adding bracing to the lower levels significantly improves seismic performance by enhancing lateral strength and reducing displacement. The research highlights that the placement and configuration of bracing are crucial in mitigating the soft story effect, thus providing effective retrofitting strategies for existing buildings to meet safety requirements and minimize earthquake damage ([PERSON] and [PERSON], 2014). [PERSON] et al. (2024) **explored** the dynamic performance of a novel tackle-damper configuration, which **combined** a viscous damper with two inclined tackles made of wire ropes. This setup **enhanced** the damper deformations and forces, **shifting** the damper's behavior from purely viscous to viscoelastic. Their experiments **revealed** that energy dissipation **occurred** from both the viscous damper and capstan friction, leading to the significant amplification of forces and energy. Deformation amplification factors **ranged** from 0.29 to 1.9, while force amplification factors **reached** between 5.3 and 58. The study **emphasized** that friction and wire rope elongation **could significantly affect** the actual amplification capabilities, suggesting that optimized designs **were necessary** to achieve ideal performance levels. However, this device **was not applicable** to limited spaces ([PERSON] and [PERSON], 2014). The evolution of fluid viscous dampers (FVDs) from passive systems to more sophisticated semi-active and adaptive systems has been a focus of recent research. [PERSON] et al. (2023) demonstrated that semi-active and adaptive dampers provide superior performance across different seismic intensities, although these advancements come with increased complexity and costs ([PERSON] et al., 2022). [PERSON] et al. (2022) investigated the seismic response of multi-story buildings equipped with FVDs, focusing on energy perspectives.