Radiation impedance matrices for rectangular interfaces within rigid baffles: Calculation methodology and applications - Pierce, A; Cleveland, R; Zampolli, M (2002)
The coupling of sound fields through a finite-sized aperture in a plane rigid baffle where the region (half-space) on one side is unbounded can be described by an integral equation which constitutes a boundary condition for the field on the other side of the aperture. Such a boundary condition, when the pressure and the normal velocity are expanded in basis functions defined over the aperture, can be recast into a matrix form relating the coefficients of the basis functions in the expansions, the principal feature being a matrix of fourfold (double-area) integrals analogous to those encountered in studies of radiation from flexible pistons in rigid baffles. A substantial analytical reduction to sums of single nonsingular integrals is derived for the elements of this radiation impedance matrix when the aperture is rectangular and the basis functions are expressible as a sum of products of exponential functions of the Cartesian coordinates of the aperture plane, with the exponential coefficients being arbitrary complex numbers. The validity of the result is substantiated by its reduction to previously published results for less general cases. Its utility is demonstrated with the example of diffraction by a square hole in a screen. © 2002 Acoustical Society of America.