# Prediction of Vibration-Mode-Induced Noise of Structure-Acoustic Coupled Systems
## 1 Introduction  
The floor impact sound generated in apartments considerably affects the comfort of residents, as indicated by research across Korea, Japan, and Europe, among other countries [1; 2; 3] Particularly, most Korean people live in apartments built with concrete and their in-door lifestyle is that they live in bare feet. This lifestyle and structure showed that with the amplification of impact sounds, which had low frequencies, and the reduction of impact sound, it was made more difficult because of the propagation characteristics of low frequency [4; 5; 6; 7; 8; 9]. Specifically, these sounds can adversely influence the physical and psychological health of the residents and lead to property-related issues. Although many researchers have examined floor impact sounds [4; 5; 6; 7; 8; 9] and the corresponding influence of floor structures of public residences [10; 11; 12; 13] using several evaluation indices [14; 15; 16; 17; 18], the problem of floor impact sounds remains to be solved. In this context, it is necessary to accurately predict floor impact sounds, especially in the Korean environment, as a relevant law named floor impact sound post-check system, and is expected to be enforced in July 2022. Several researchers have attempted to predict the floor impact noise using the impedance methods and finite element method (FEM) [19], finite difference time domain (FDTD) [20; 21; 22; 23; 24], and statistical energy analysis method (SEA) [25]; however, the accuracy of these methods is limited. In general, the impact generated in a source room is transmitted through a slab in the form of vibrations and converted to sound on the ceiling surface. According to [PERSON] et al. [26], the noise with high frequencies can be represented by the vibrationmode. Furthermore, the maximum sound level of heavy impact sound pertains to the acoustic mode, which is influenced by vibration transferred through a structure or wall, depending on the frequencies [27]. Therefore, to predict the sound level in a room, the relationship between the vibration and sound must be examined. In practice, structural vibrations generated a unique sound field in the acoustic domain according to the sound environment and structural characteristics. The sound field induced by the interaction between the vibration and fluid at the acoustic-structure boundary depends on the level of coupling; each coupling is expected to generate a sound field that is different from the corresponding individual vibration and sound fields. The heavy weight floor impact sound encountered in apartment buildings is representative of the structure-induced sound pressure often observed in structure-acoustic physical spaces. Since this sound pressure is generated by the vibration of a structure (slab), the two physical quantities are expected to be strongly correlated. In an acoustic domain with structure and sound coupling, the prediction of structural-vibration-induced sound pressure or noise is expected to involve uncertainties owing to the variables in the sound environment (e.g., size and shape of the structure and acoustic boundary conditions). Nevertheless, the correlation between the two physical quantities is widely investigated owing to the ease of vibration measurement, which can facilitate comprehensive noise control by the vibration magnitude and realization of noise alarm functions. Moreover, as mentioned previously, the introduction of the floor impact sound post-verification system has necessitated the development of a method to predict the noise in a room caused by floor vibrations by estimating the floor impact sound in the design stage and to establish noise-reduction measures. Certain researchers attempted to predict the noise by measuring the slab vibration to examine the correlation between the slab vibration and generated noise levels [28; 29]. The light-weight floor impact sounds exhibited an extremely high correlation coefficient (approximately 0.95).