On reconstruction of acoustic pressure fields using the HELS method

Abstract

The Helmholtz equation-least squares (HELS) method was recently developed by Wang and Wu [J. Acoust. Soc. Am. 102, 2020–2032 (1997)] to reconstruct the acoustic pressures generated by an arbitrary vibrating structure. In this method the acoustic pressures are expressed in terms of an expansion of ‘‘acoustic modes.’’ The coefficients associated with these acoustic modes are determined by requiring the assumed-form solution to satisfy the pressure boundary condition at measurement points. The errors incurred in this process are minimized by the least-squares method. The advantages of this method are that (1) acoustic pressures can be reconstructed over the entire surface; (2) solutions thus obtained are unique; and (3) efficiency of numerical computation is high, because the number of measurements is determined by that of expansion terms, which is small when a right coordinate system is selected for a particular source geometry under consideration. Such an approach is applicable to both exterior and interior regions. For exterior problems, the reconstructed acoustic pressures can be accurate when the points fall outside the minimum circumscribing spheroidal surface which encloses the vibrating surface, but approximate when they are inside. For interior problems, the accuracy of reconstruction is high because the entire region is inside the minimum circumscribing spheroidal surface. In both cases, the accuracy of reconstruction is limited by excitation frequencies, which is inherent in all expansion theories. [Work supported by NSF.]