Analysis of noise attenuation through soft vibrating barriers: an analytical investigation

In this article, the impact of fluid flow and vibration on the acoustics of a subsonic flow is examined. Specifically, it focuses on the noise generated by a convective gust in uniform flow that is scattered by a vibrating plate of limited size. The study analyzes the interaction between acoustics and structures by considering the scattering of sound waves by a soft finite barrier. To achieve this, the Wiener-Hopf technique is utilized for the analytical treatment of the acoustic model. The approach involves performing temporal and spatial Fourier transforms on the governing convective boundary value problem, then formulating the resulting Wiener-Hopf equations. The product decomposition theorem, an extended version of Liouville's theorem, and analytic continuation are employed to solve these equations. Finally, the scattered potential integral equations are computed asymptotically. This study can be significant for understanding the acoustic properties of structures and how they interact with fluid flow in subsonic environments, which could have applications in fields such as aerospace engineering, noise reduction, and structural acoustics.