# Vibro-Acoustic Numerical Simulation for Analyzing Floor Noise of a Multi-Unit Residential Structure
## 3 An Illustrative Example
### Numerical Simulations and Comparisons
From the results of the vibration analysis in Figures 8 and 9, it can be concluded that multi-unit residential buildings with a repetitive structural form like the test structure of this study will generate the largest vibration on the target floor and the second largest vibration on the next upper and lower floors. It is also clear that the magnitude of vibration decreases with increasing distance from the target floor. The same analysis was conducted for the remaining floors. Figure 10 compares the magnitudes of vibration between the target floors to which the impact source was applied. Both the 2 nd floor and the roof floor (18F) could transmit the generated vibration only in either the upper or lower direction, which was a different condition from the other floors. Consequently, both the 2 nd floor and the roof floor showed a marginally different result, as shown in Figure 10. Additionally, Figure 11 depicts the largest magnitude of the structural vibration of five floors. From Figure 11, it can be seen that the  
Figure 8: Results of vibration response to impact load on floor 11F. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Name**} & \multicolumn{2}{c}{**Concrete**} \\ \cline{2-3}  & **Low Story (C27)** & **Upper Story (C24)** \\ \hline Modulus of Elasticity (GPa) & 26.7 & 25.8 \\ Density (\(\rho\), kg/m\({}^{3}\)) & 2400.0 & 2400.0 \\ Poisson’s Ratio (\(\
u\)) & 0.167 & 0.167 \\ Acoustic Impedance (Z, MRayl) & 8.0 & 8.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material property of the specimen. acceleration shape of the five floors with respect to the frequency has shifted to the left as the height of the floor rises, which is due to the boundary condition of the test structure to which the bottom is fixed. Figure 10: Results of the vibration response when the impact load was applied to five floors; (**a**) At narrow band frequency; (**b**) at 1/3 octave band frequency. Figure 9: Results of the response when the impact load was applied to: (**a**) Fifth floor; (**b**) 15 th floor. The acoustic analysis was performed using results of the vibration analysis when the impact source was applied to the 11 th floor of the test structure. Then, results of the acoustic analysis were analyzed and compared with the field measurements. As in the field measurements, the acoustic analysis results of the five microphones are analyzed with respect to the 1/3 octave band frequency, as shown in Figure 11. As a result of the above vibration analysis, it can be seen that the floor noise, which is sound pressure level, decreases as the frequency increases. As shown in Figure 12, a comparison between the vibro-acoustic analyses results and the field measurements results with regard to the 1/1 octave band revealed that the numerical simulations using the impact forces are very similar to the field measurements results. Figure 11: Acoustic response of the vibro-acoustic simulations for five microphones and its mean value. Figure 12: Comparison of the acoustic response between the simulations and field measurements. Table 4 presents the comparison of the 1/1 octave band and SNQ-based evaluations for the results of both the field measurements and the numerical simulations. The results of the numerical simulations showed a higher value than that of the field measurements, except at 500 Hz. Consequently, the former had an SNQ value of 55 dB, which was just higher than that of the latter case by 4 dB. It should be noted that the difference of 4 dB can be explained, as: (1) The reinforcing steel bars in the floors, walls, and columns have been neglected in the numerical model; (2) the concrete material is not the perfectly isotropic material, which means that the condition of the numerical model is different than that of the real structures; and (3) there are uncertainties in the field measurements. Therefore, these can all be contributing causes for the difference of 4 dB.