## 1 Introduction
The piston plate in a VD has an orifice that allows viscous fluid to flow between compartments, affecting the movement of the piston plate. The fluid used is typically incompressible, which means it does not compress easily. As the piston plate moves, the fluid within the barrel begins to move, generating compressive force. The movement of the piston plate changes the volume of viscous fluid in one compartment. Smaller compartments generate higher force compared to larger ones. [PERSON] and [PERSON] (2016) found that the speed of the piston plate's movement is directly related to the force generated. Additionally, the fluid's viscosity and the orifice diameter affect the force output. Generally, when supplementary viscous dampers are installed in a frame, they can reduce movement from the bottom floor by 4% and up to 32% for the top floor [30]. The frequency of natural disasters, such as earthquakes, tsunamis, and tornadoes, has increased annually. These events can have significant impacts on buildings and structures. Buildings unable to withstand seismic tremors may collapse due to excessive movement. Failures in building design have driven advancements in more resilient building technologies, which is a growing area of research. A key failure factor is the collapse of building structures when they are subjected to loads beyond their design capacity, leading to excessive movement. In such conditions, structural components may fail to control deformation and dissipate energy effectively, leading to exhaustion of the structure, especially at the joints between components. VDs are easier to install than many other types of dampers due to their relatively small size. [PERSON] and [PERSON] (2003) demonstrated that viscous dampers do not require a large installation area, making them suitable for retrofitting existing buildings without major difficulty. However, installing dampers in existing buildings can be challenging because strengthening and retrofitting often involves installing new, larger, and heavier dampers than the original ones. Increased damper dimensions may not fit in the same space, necessitating significant repairs for installation. For offshore structures with rounded components, damper installation is also costly because it requires specialized skills and equipment [31]. The installation area required for tuned liquid dampers (TLDs) is dependent on the dimensions of the water tank and its working area. Larger tanks can dissipate more energy, but they also require more space. In existing structures, space is often limited, making it difficult to install new TLDs after seismic events due to the increased tank size and lack of available space. Finding suitable space in existing structures may require additional modifications. The scenario, however, differs at jetties, yards, and ports. These buildings must be capable of withstanding the substantial impact forces exerted by large vessels. Given the high levels of energy they encounter, the dampers in these structures need to have a high capacity to absorb these impacts. To achieve a high-capacity damper, its size must be large, which poses challenges for installation due to limited working areas and the damper's unwieldy size. The ideal location for installing a conventional VD would be under the floor near the seawater surface. However, this positioning necessitates regular maintenance due to exposure to harsh marine conditions. The integrity of offshore structures is heavily influenced by design considerations for environmental loads such as wind, waves, and earthquakes. These structures must be able to withstand high-magnitude loads with return periods of 50 or 100 years. According to studies by [PERSON] et al. (2007), the addition of damping devices can significantly enhance the stability of offshore structures. These studies demonstrated that oscillatory motions induced by vibrations present a significant load, and the use of tuned liquid dampers showed promising results.