Reconstructing the Acoustic Pressure Field Based on Oblate Spheroidal Coordinates

Abstract

A new acoustic reconstructing method based on oblate spheroidal coordinates is proposed and deduced in this paper. The acoustic pressures of whole acoustic field are expressed by the product of the coefficients and the conventional interpolate polynomial. Once the coefficients are specified by the pressures of the measured points, the least-squares method and the singular value decomposition (SVD) method, the whole acoustic field can be reconstructed. The traditional HELS method is most suitable for reconstructing pressures radiated a spherical source or sources with a characteristic aspect ratio x: y: z close to 1:1:1. While the new method proposed in this paper is suitable for the acoustic sources with a characteristic aspect ratio y: z close to 1:1 and shorter z, which extends the appropriate application domain of traditional HELS largely. The reconstructing examples of a dilating sphere and an oblate spheroid source show that the new method is feasible and efficient. Keywordsacoustic reconstructing method; Helmholtz equation-least-squares (HELS) method; oblate spheroidal coordinates; acoustic pressure field;