Sound scattering by cylinders of noncircular cross section: A conformal mapping approach
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A new method for predicting the far-field scattered pressure due to a plane wave incident upon an infinitely long cylinder of noncircular cross section is presented. The method, referred to herein as the Fourier matching method (FMM), involves conformally mapping the exterior and interior of a closed surface to a semi-infinite strip. This method is new in that the boundary conditions are satisfied using constraints described in the new angular variable. The resultant formulation is numerically efficient (much more so than the T-matrix method under certain conditions, for example) and works well for both small and large deviations from a circular cross section, as well as penetrable and impenetrable materials. Furthermore, the basis functions generated in the calculation can also improve the efficiency of other methods such as the T-matrix method. Example calculations are presented for elliptic, square, and three-leaf clover cross sections for several types of boundary conditions. In all cases, the results compare extremely well with exact or high-frequency asymptotic results.