# Sound Radiation of Aerodynamically Excited Flat Plates into Cavities
## 1 Introduction  
There are noise sources everywhere in our environment, and these sounds are transferred in different ways to the human ear. The simplified generic model subject to this investigation reflects the type of sound excitation and transmission that occurs in numerous applications, e.g. in passenger vehicles, such as cars, buses, trains or planes. This undesirable sound is caused by excited flat structure elements. Today, people are constantly exposed to continuous noise which constitutes one of the most serious problems of our time [1]. Therefore, a growing need for personal acoustic shielding arises. The increasing travel time for great distances is indirectly leading to higher driving velocities to save time in turn. Thus, the flow noise develops to the dominating driving noise. In this context, there are numerous scientific studies discussing individual issues of the noise origination without considering the entire effect chain, starting with excitation, over the sound radiation und transmission to the sound detection. Recent studies analyzed the flow-induced vibration of a plate with a crosswise prefixed obstacle plate and an additional external exciter with a varying frequency and amplitude [2]. External forces often have an effect on flow-excited plates. It turned out that both excitations are influencing the dynamics of the system. The frequencies of both test modes appear in the frequency spectrum at a low amplitude of the external harmonic excitation, whereas the external excitation in a coupled system is prevailing at a higher amplitude. Concerning the sound radiation into a room, there were vibroacoustical analytical investigations on a model of a railway vehicle body [3]. The structure-induced noise radiation of flexible floor panels was analyzed and the natural frequencies and the sound pressure field inside the cavity were analytically determined. The result of the study is that significant resonance peaks arise from two concentrated forces on the plate if the dominant excitation frequency approaches the natural frequencies of the system. Moreover, the rise of the flow velocity led to an increase in the sound pressure inside the cavity. Regarding the spatial distribution of the sound pressure, it was found that the sound pressure above the excitation points takes remarkably higher values. Numerous cases regarding the flow over different obstacles have already been investigated. Low importance has been attached to the sound radiation of a plate and the coupled distribution inside a cavity yet. However, two novel studies considering this subject were published this year. [PERSON] et al. [4] focussed on the analytical modeling of a three-dimensional coupled acoustic system consisting of a cavity with a coupled flexible plate and a semi-infinite expanded field. The excitation of the system, including acoustic and structural-acoustic coupling, is generated inside the cavity by a point source. A solution method was found to predict the dynamic behavior of the entire system using Fourier series to express the sound pressure and the displacement of the plate. The results are validated through numerical simulations. This approach examined the issue which will be covered in detail in this paper, but only in an analytical way with an excitation in reverse direction without the influence of an external flow. [PERSON] and [PERSON] [5] investigated the sound transmission into and radiation from a cavity through a flexible plate structure in a noisy/thermal environment in a supersonic flow. Using nonlinear models for the pre- and the postflutter regions, equations for the flexible panel, cavity acoustics and turbulent boundary layer are developed. Based on several approaches and theories, the resulting equations are solved numerically. The results for the postflutter domain are high sound pressure levels in the lower-frequency regions and a Helmholtz resonator condition with homogenous sound pressure distribution inside the cavity.