# Vibro-Acoustic Numerical Simulation for Analyzing Floor Noise of a Multi-Unit Residential Structure
## 3 An Illustrative Example
### Numerical Simulations and Comparisons  
Figure 5(a) shows a numerical model of the 17-story structure. Table 2 shows the meshing information of the numerical model. The excitation location of the impact source and the location of the five indoor microphones for noise measurements were numerically installed at the exact same locations used in the field measurements, shown in Figure 5(b). The test structure has 17 floors and can be categorized into a high-rise structure. Therefore, two concrete materials are used, i.e., C27 for the lower parts (1 st-10 th's floors, walls, and columns, and 11 th's floor) and C24 for the upper parts (11 th's walls and columns, and 12 th roof's floors, walls, and columns), respectively. It should be noted that the reinforcing steel bars in the floors, walls, and columns are neglected in this study. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **No.** & **Type** \\ \hline Nodes & 274,900 & - \\
2D Frame Element & 10,812 & Structure \\
2D Quad Element & 273,785 & Structure \\
3D Tetra Element & 46,859 & Acoustic \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The meshing information of the target structure. Figure 5: Acoustic response of the field measurements for five microphones and its 1/3 octave band frequency. Figure 7 shows the structural and acoustic mesh of the target area, shown in Figure 4b. The real structure has walls, windows, and doors, etc. In this numerical model, walls and columns are modeled as structural elements such as frames and plates, etc. In addition, windows, doors, and other empty spaces are modeled as an acoustic panel which has absorbent property. The target areas are modeled as 3d tetra elements. Table 3 presents the material properties for the numerical models [37, 38, 39]. The structural vibration analysis was carried to the entire structure, and then the acoustic analysis was conducted only for the living room area. To identify the magnitude of vibration and its variation when being transmitted to the upper and lower floors (according to the position of the impact load), a vibro-acoustic analysis was conducted by assuming that the impact load (the impact source being the bang machine at MC#3 in Figure 6b) was applied sequentially from the floor slab of the 2 nd floor (top slab of the 1 st floor) to the top slab of the 18 th floor (ro  
Figure 6: Graphical representation of the test structure: (**a**) The computational model; (**b**) microphone’s location for acoustic analysis. Figure 7: Schematic overview of the structural and acoustic mesh of the target area. Figure 8 shows an example case of applying the impact load to the floor slab of the 11 th floor, and the results of the vibration analysis from the floor slab of the 2 nd floor to the roof slab of the 18 th floor. The largest vibration response was produced at the 11 th floor, which was the target floor of the impact source. The second largest responses were produced at the 10 th floor, which is the next vertical upper floor, and the 12 th floor, which is the next vertical lower floor. The next largest vibration responses were produced at the 9 th and 13 th floors, which were the second next upper and lower floors, respectively. The 10 th and 12 th floors showed very similar results, as did the 9 th and 13 th floors. It is very clear that when an impact source is applied to the floor slab of an upper floor, as the largest vibration occurs to the target floor. After the vibration is transmitted equally to both the upper and lower parts, the transmitted energy dissipates gradually, and the other floors generate less vibration. An additional vibration analysis was conducted for the 5 th floor, in the lower portion of the overall building, and for the 15 th floor, in the higher portion of the overall building (see Figure 9). Figures 8 and 9 show that the target floor of the impact source generated the largest vibrations, which were then transmitted to the vertical upper and lower floors.