Acoustic diffraction by a finite strip in convected medium is theoretically analyzed as a fundamental study of linear cascade-turbulence interaction and airfoil-gust interaction phenomena which are important issues on aeroacoustics. The analysis is mainly focused on the rigorous mathematical procedures from the formulation of concise integral equation to the acquisition of exact solution. Since this finite diffraction problem belongs to a 3-part mixed boundary value problem of convective wave equation, its value is of great importance from the viewpoint of mathematical methodologies as well as the viewpoint of physical understanding of the simplest multiple diffraction phenomena. Therefore, the aims of this study are (i) to formulate an exact and concise equation, (ii) to obtain an exact solution in handy form and (iii) to interpret the physical meaning of mathematical solution.
On the formulation, the exactness comes from the use of a function theoretic method called Wiener-Hopf technique in complex domain and the conciseness comes from the uses of Prandtl-Glauert transform and some mathematical manipulations of decoupling the simultaneous integral equations resulted from the Wiener-Hopf procedure.
On the acquisition of solution, since the finiteness of strip geometry inevitably yields a multi-valued kernel in integral equation, author proposes a solution technique which is mathematically rigorous and yields a series solution whose eigenfunction is generalized gamma function with the application of author’s new formulas for this special function. The convergence analysis of the solution is performed in complex domain along the path of integration of inverse Fourier transform. We could observe that our series solution shows fast convergence in high frequency range.
Finally, by exact and asymptotic evaluations of inverse Fourier transform, the scattered acoustic fields are visualized and each term of the solution is interpreted with its physical meaning as...