Abstract
Van Bladel has reduced the problem of low-frequency scattering through an aperture in a rigid screen to a sequence of static integral equations. Analytical solutions are known at the moment for a circular and an elliptic aperture only. A new analytical method is proposed here which is valid for apertures of arbitrary shape. The method is based on an integral representation for the reciprocal distance between two points, which was previously obtained by the author. Specific approximate formulae are derived for evaluating the average value of the first term in the low-frequency expansion for an aperture in the shape of a polygon, a triangle, a rectangle, a rhombus, a circular sector and a circular segment. All the formulae are checked against the numerical solutions known in the literature, and a good accuracy is confirmed. The second and the third terms of the low-frequency expansion can be derived in a similar manner, and the related formulae are to be publlshed later.
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