## 1 Introduction  
In the 1970s, the Chinese-American scholar [PERSON] systematically introduced structural vibration control technology, providing new insights for global seismic design of structures [1]. Subsequently, researchers worldwide conducted in-depth studies on structural damping systems and seismic damping technologies. In the span of over five decades, the fields of damping materials, damper technology, and innovative energy dissipation systems have seen remarkable growth. The incorporation of damping materials and dampers has become a critical component in the realms of structural passive, active, and semi-active control strategies, now extensively implemented in key construction projects across the globe. Taipei 101 utilizes a pendulum-type damper to mitigate vibrations by swinging and dissipating energy in response to seismic or wind forces, effectively reducing the structural oscillations of the building's core [2]. Other notable structures, such as the Suqian City Construction Building, Seattle's T-Mobile Park, Unit 3 of the Qinshan Nuclear Power Plant, and a Romanian oil refinery, have implemented viscous dampers for vibration attenuation and energy dissipation [3]. The Shanghai Tower utilizes an eddy current tuned mass damper, marking a significant advancement from conventional viscous damper technology [4]. The steel energy-dissipating double-link beam dampers employed in the China Zur Building effectively counteract the stiffness degradation of concrete beams, thereby markedly augmenting the structure's seismic resilience [5]. Since the initiation of reform and opening-up policies, China has witnessed a rapid expansion in its hydropower and water conservancy construction sector, culminating in a series of high-caliber projects and the attainment of numerous innovative milestones on the global stage in dam engineering. Consequently, China has become the nation with the largest number of dams. Concurrently, the sector has had to confront the formidable challenge of how these massive dam structures, with their significant mass and volume, can effectively resist the forces of seismic loads. High earth-rockfill dams enhance their seismic performance through the design of geosynthetic-reinforced soil structures and the application of reinforcement and nail techniques [6]. Tailings dams employ toe berm construction using rockfill to effectively prevent potential instability and failure of the dam structure [7]. High arch dams ensure seismic resistance by optimizing dam structures, arranging seismic-resistant reinforcement bars, and strengthening joint structures [8]. Additionally, novel damage assessment methods are used to evaluate the safety of gravity dams [9]. These methods involve allowing a certain degree of deformation in the dam body through the installation of expansion and deformation joints, reducing the response to seismic actions. The use of new materials, such as fiber-reinforced materials, also improves the structure's toughness and seismic performance. High concrete dams face a dual challenge of seismic loads and reservoir water pressure, for which effective solutions remain elusive [10]. Switzerland's extensive dam safety assessments over the past 15 years have revealed that current seismic resistance technologies in dams are outdated [11]. The growing complexity of dam siting and height has rendered existing seismic measures insufficient, prompting a new research focus on developing cost-effective damping materials and designing appropriate dampers for dam structures. Leveraging the remarkable property of variable stiffness inherent in shape-memory alloy (SMA) smart materials, [PERSON], [PERSON], and colleagues have developed a novel SMA damper. The study details the damper's structural composition and operational mechanism, presents the corresponding mechanical model, and validates the model's accuracy through numerical simulations [12]. The effectiveness of this system was confirmed by comparing its performance to conventional seismic mitigation methods.