# Prediction of Vibration-Mode-Induced Noise of Structure-Acoustic Coupled Systems
## 1 Introduction
In contrast, the correlation coefficient for heavy-weight floor impact sound varied between 0.46 and 0.9, which indicated that the use of the acceleration level to evaluate the noise between floors was associated with a limited accuracy. Other researchers used the relationship between the vibration and acoustic modes to increase the correlation between the vibration and heavy-weight floor impact sound [30]. The correlation between the vibration and sound pressure levels in a free field was extremely high (0.91), but that in a structure-acoustic combined space varied owing to the uncertainties in the modal response contribution levels and modal characteristics of the sound environment containing the structure. Several studies were conducted to examine the structural vibration and sound. For example, [PERSON] et al. [31] used the eigenvalue method to analyze a coupled system, and [PERSON] et al. [32] used the Trefftz approach to predict the wave propagation in a coupled system. FEM and other methods were also used to examine the influence of vibration-acoustic coupling on structures [33; 34; 35; 36]. Notably, although these studies clarified the correlation between the structural vibration and acoustic domain noise, a quantitative causal relationship between the two physical quantities remains to be presented. Considering these aspects, this study was aimed at examining the mechanism by which structural vibration was induced as noise from a structure-acoustic coupled system. Moreover, the influence of the vibration and acoustic modal parameters, which reflect the sound environment, on the formation of the acoustic mode in a receiving room was evaluated to predict the noise in the receiving room from the structural vibration mode. A time-domain numerical analysis was performed to assess the plausibility of the structural vibration-acoustic modal response predictions. In general, compared to a frequency-domain analysis, which could be performed to examine a stationary sound field, a time-domain analysis was more suitable for investigating the vibration induced by an impact load or the characteristics of the sound pressure induced by such vibrations (nonstationary signals, such as heavy-weight floor impact sound). Additionally, since raw data of the time history could be incorporated in the time-domain analysis, the maximum responses such as the maximum vibration and sound pressure against the impact load could be determined. A secondary analysis, such as a 1/3 octave band spectrum analysis of the time zone at the point of maximum response occurrence, can be performed to determine the maximum acceleration level and sound pressure level. In this study, the numerical analysis was performed on a reverberation chamber with a shell structure on one side. A reverberation chamber with this configuration was considered because it can provide ideal sound boundary conditions, enabling clear observation of the relationship between the vibration and noise. The shell structure was simulated to allow the induction of vibration by the impact load, leading to the generation of heavy-weight impact sound in the reverberation chamber. The time histories of the vibration and sound pressure at the measurement locations on the shell and in the reverberation chamber were extracted, and the vibration and acoustic modes were identified by applying mode decomposition to validate the noise-induced acoustic mode formation characteristics and proposed noise prediction framework.