## 3 Detailed Design of Viscous Plane Damper  
The newly proposed viscous plane damper is square-shaped and consists of a box barrel (cylindrical), piston plate, piston rod, head mounting, and bottom mounting. The key difference between typical viscous dampers and the new viscous plane damper lies in the shape of the piston plate and box barrel, which has been changed from the conventional circular form to a square shape. Additionally, the cross-sectional area of the damper device and the configuration of the orifices on the piston plate have been redesigned to achieve the desired performance and functionality. Figure 1 illustrates the detailed configurations of both a conventional viscous damper and the newly developed viscous plane damper used in this study. The new viscous plane damper is designed with simple components to facilitate easy manufacturing and installation, particularly in limited-space areas. The damper's components are also separate to ensure easy handling and transportation. Upon installation, these components can be easily assembled to form the complete viscous plane damper. The most crucial component of the viscous plane damper is the piston plate, which is square-shaped and features tiny holes serving as orifices. These orifices generally allow the viscous fluid to transfer from one side to the other. In this study, different configurations and various orifice diameters were explored to optimize the damper's performance. The positioning of the orifices on the piston plate is shown in Figure 2. Three distinct configurations were tested, labeled A, B, and C. Configuration A has 16 holes arranged in a 4 \(\times\) 4 matrix. Configurations B and C each have 4 holes but with different arrangements and positions on the piston plate. Configuration A serves as the control sample, providing a baseline prediction of fluid flow behavior. Additionally, each configuration was evaluated with four different orifice diameters, 1 mm, 2 mm, 5 mm, and 10 mm, to assess the impact of orifice diameter on pressure drop and the performance of the viscous plane damper. As shown in Table 1, the total cross-sectional open area of the orifices in Configuration A is four times larger than that in Configurations B and C. Consequently, the total open area in Configurations B and C is only 25% of that in Configuration A. Furthermore, the total open area of a 10 mm diameter orifice is four times greater than that of a 5 mm diameter orifice across all configurations. The total cross-sectional open area for a 5 mm diameter orifice in Configuration A is nearly equivalent to that of Configurations B and C. Overall, various orifice diameters were analyzed to determine the behavior of the viscous fluid as it flowed through the orifices and evaluate the effect of pressure drop on the damping force and damping ratio. Figure 1: Configuration of conventional viscous damper and proposed viscous plane damper. Figure 2: Configuration of the orifices on the piston plate. The schematic drawing of the developed viscous plane damper is presented in Figure 3. As shown in the figure, the new viscous plane damper features a distinct shape and dimensions. The length or height of the viscous plane damper is shorter compared to that of a typical viscous damper, making it suitable for installation in confined spaces. Additionally, the new viscous plane damper is wider than the diameter of a conventional viscous damper, providing an adequate area for the cylinder cube to generate pressure drop and damping force. The new design of the viscous plane damper consists of separate components: head mounting, box barrel, piston rod, piston plate, and bottom mounting. The mountings are used to attach the damper to the structural elements. The piston plate and piston rod are installed inside the box barrel. The barrel is secured to the bottom mounting with bolts and nuts. Additionally, the piston rod connects the piston plate to the head mounting. The mountings are designed to move parallel to the structural movement.