Reconstruction of acoustic radiation from a finite object in nonfree space

The near-field acoustic holography (NAH) techniques developed so far have focused on reconstruction of acoustic radiation from a vibrating structure in either an unbounded exterior region or an enclosed region so that it can be solved as an interior problem. In practice, many vibrating structures are mounted on a solid foundation or in the vicinity of reflecting surfaces. For NAH to become a robust diagnostic tool, the effect of acoustic pressure reflection from nearby surfaces must be considered. In this paper, the Helmholtz equation least-squares (HELS) method [Wu, J. Acoust. Soc. Am. 107, 2511–2522 (2000)] will be modified which expresses the field acoustic pressure as a superposition of both out-going and in-coming spherical waves. The latter will be used to approximate the acoustic pressure reflection from nearby surfaces. To guarantee a convergence of the reconstructed acoustic field, a constrained minimization will be conducted with respect to the expansion functions to determine the optimal numbers of expansion terms for both out-going and in-coming waves. This concept will also be extended to reconstruction of acoustic radiation from an arbitrarily shaped vibrating structure for which the conventional HELS formulation has been shown to have difficulties to yield satisfactory reconstruction. [Work supported by NSF.]