## 2 Dynamic Model of the System
### Analysis Modeling  
The FSI analysis requires a three-dimensional (3D) modeling. Therefore, in this study, a 3D model of the scrubber shown in Figure 1 was constructed using Solidworks based on the 2D drawings of the scrubbers installed in the building. For the pump, a 3D model was constructed using the same specifications provided by the manufacturer. In addition, the models were modified for the analysis using a Fusion 360 program, as shown in Figure 3. If the models are not corrected, the error of the shape of the element around the pump and the number of nodes of the finite element method (FEM) body increase rapidly in a specific part, making it impossible to obtain correct analysis data [16; 17]. Therefore, unnecessary elements that do not affect the analysis were removed, and the model was modified in a form suitable for the analysis. In the modified model, a mesh procedure was performed to obtain vibration data for the remaining bodies except the main tower. Figure 3: A multi-flexible body and its data points. Figure 2: Schematic of the fluid structure interaction (FSI) analysis method. In the actual field, the vibration has been confirmed to be most severe around the pump, whereas vibration was hardly felt in the main tower even when it was in operation. The use of speed sensors results in irregularly measured data owing to the interference of the surrounding environment and cannot be used as verified data, so it was not referenced in this study. Therefore, to proceed with the analysis in the form of a multi-flexible body, a mesh procedure was performed only for the water tank, pump, and pipe body. The total number of grids of the Finite element body was 683,813, and if mesh was performed on the main tower, the number of grids increases significantly and the analysis time may increase excessively. Therefore, the main tower was considered to be a rigid body to significantly reduce the overall analysis time. Moreover, data can be rapidly obtained by focusing on the structure where vibration was generated. Figure 3 shows six locations around the pump where the greatest vibration is felt in the field, and the vibration data for these locations were obtained using analysis. For elements in contact between bodies, the hertzian contact law infers that if the elastic modulus value is lower than that of steel, it is unnecessary for the stiffness value to exceed 100,000 N/mm [18]. The physical properties of the structure employed in this research are presented in Table 1, and the elastic moduli of the parts were lower than that of steel, so the ranges of stiffness and damping coefficients are calculated and presented in Table 2. If the Stiffness value is too low, an accurate contact between the bodies cannot be achieved, whereas if the value is too high, the analysis time significantly increases, so an appropriate range was calculated based on the hertzian contact law. This range is the range obtained through the test by applying values to the analysis program. Both the pump and pipe were composed of FRP, and the water tank was composed of steel to enable it withstand the weight of the pump as the total weight, including that of the motor of the pump, is 472 kg. In addition, the physical properties of the liquid were set to that of a general water material, as shown in Table 3.  
In the state in which the fluid is saturated, there is no significant change in the data over time, and the two-way FSI analysis takes a long time to analyze, so 3 s of data was obtained for 4-7 s, which is in the saturated state. The pump is placed on a water tank, and since the water is pulled up, the largest vibration is generated in the direction of gravity. This was the same when the maximum reaction force of the pump operated through analysis was calculated, and the maximum reaction force for the direction of gravity is as shown in Figure 6. The maximum reaction force of the pump obtained at this time is the reaction force value generated when the cleaning liquid was pulled up by the impeller while the fluid is satiated.