Reconstruction of acoustic radiation from vibrating objects in a half space using hybrid nearfield acoustical holography

Abstract

Hybrid nearfield acoustical holography (NAH) [Wu, J. Acoust. Soc. Am. 113, 2252 (2003)] is utilized to reconstruct the vibro-acoustic fields generated by vibrating structures in half space. These hybrid formulations are derived from a modified Helmholtz equation least-squares method, where the field acoustic pressure is expanded in terms of both outgoing and incoming spherical waves, and the Helmholtz integral formulations implemented by the boundary element method (BEM). To overcome the ill-conditioning difficulties in the resultant matrix equations, regularization techniques such as the method of Tikhonov and generalized cross validation are employed. The main advantage of this hybrid approach is that satisfactory reconstruction can be obtained with relatively few acoustic pressure measurements taken over a conformal surface around the source. This is because a large portion of the input data is regenerated by the modified HELS, but not actually measured. Hence, the efficiency of reconstruction is enhanced. If the same number of measurements is used in an inverse BEM code, the reconstructed vibro-acoustic quantities on the source surface may be distorted. Numerical examples of a dilating and an oscillating sphere and a cylinder with spherical endcaps in half space are demonstrated. [Work supported by NSF.]