Abstract
This paper describes verification and examination in applying Mathieu functions for constructing Non-compact Green functions for wing-like body. First the paper reviews composition of plane wave and scattering wave by Bessel functions for cylindrical body. Key idea is introduction of Bessel functions and Hankel functions in the composition. Similarity of Mathieu functions in elliptic cylindrical coordinates with Bessel functions in circular cylindrical coordinates is utilized for constructing the Non-compact Green's function for wing-like bodies. Adequacy of Mathieu Functions are examined in their behavior in neighborhood of body surface. Lastly the paper discusses application of the new Non-compact Green's functions to designing low-noise wing with porous surface.
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