Introduction of complex layer analysis (CLA) for acoustic radiation problems

The pressure radiated by a planar vibrating surface with a prescribed harmonic time‐varying surface velocity can be represented as the inverse Fourier transform of the product of the velocity transform and the spectral form of the acoustic surface impedance. This integral representation usually cannot be evaluated in closed form, but can, however, be evaluated asymptotically in the far field, i.e., at field points large compared to the acoustic wavelength. In this note a novel approach, ‘‘complex layer analysis’’ (CLA) is introduced which involves an approximation of the acoustic impedance in terms of a rational function. Contour integration is then used to obtain an explicit expression for the near‐field pressure distribution as a sum of waves propagating with wave numbers corresponding to the poles of the approximate acoustic impedance. Such an expression makes explicit the notion of pressure‐field generation localizing to points of discontinuity in the velocity distribution. [Work supported by the Card...