Near-field acoustic holography in conical coordinates

Abstract

Near-field acoustical holography (NAH) techniques can be optimized if the method capitalizes on the geometry of the noise source under investigation. Helmholtz-equation least squares method (HELS) uses the solutions of Helmholtz equation in spherical coordinates as basis functions for the pressure field. HELS is an efficient NAH technique if the source and the measurement surfaces are spherical in nature. For nonspherical cases, such as radiation from a plate or bar, it takes a large number of functions to represent the field. In these cases, there is also a question about where to place the origin of the wave functions. In search of a HELS-type method that could be applied to nonspherical sources, a study into the features of conical coordinates has been conducted. Because Helmholtz equation is separable in conical coordinates, the solutions can be used, in a manner similar to HELS, as basis functions to represent the pressure field. For conical coordinates, the basis functions are spherical Hankel functions and Lame functions. Thus, for a conical source, a HELS-type formulation in conical coordinates could provide a natural choice for near-field acoustical holography.[Work supported by Blue Ridge Research and Consulting and Air Force Research Laboratory.]