Theoretical Model of Scattering from Serrated Flat Plate

In this paper we will present a theoretical model to study sound scattering from the most simplified airfoil (a semi-infinite flat plate) but with serrations. The key contribution of our work is the analytical description of the acoustic scattering effect of serrations by incorporating Fourier series expansion and Wiener-Hopf method. In particular, we describe periodical variations of the serrations by using Fourier series that accurately represent the geometrical layout of serrations in the lateral direction. Then, a Wiener-Hopf based theoretical model will be established to analytical examine the scattered sound field from the serrated plate. The associated matrix Wiener-Hopf kernel will be given and a closed-form solution could be obtained after adopting a couple of appropriate approximations. Some primitive numerical tests are being performed to validate the proposed theoretical model, which, then, will be used to study more complicated and interesting layouts of serrations. The whole work should be of practical importance in the development of silent aircraft and more details will be given in the final paper.