Analysis of reconstruction of radiated acoustic pressure fields by using the HELS method

Abstract

This paper presents a detailed analysis of reconstruction of the acoustic pressure fields radiated from a partially vibrating sphere by using the Helmholtz equation-least squares (HELS) method [Z. Wang and S. F. Wu, J. Acoust. Soc. Am. 102, 2020–2032 (1997); 104, 2054–2060 (1998)]. The objectives of this study are to gain insight into an acoustic inverse problem and to develop guidelines that may be helpful in the future reconstruction work. Because of the complexities involved, many questions such as where and how many measurements should be taken, how many expansion terms are necessary for a given number of measurements, etc., remain unanswered. These questions will be tackled here. The reasons for selecting a partially vibrating sphere are twofold: (1) the resulting acoustic pressure field contains a very pronounced near-field effect; and (2) analytic results are known so the reconstructed acoustic pressures can be checked rigorously. The impact of a loss of the near-field effect on reconstruction will be investigated. The effects of measurement distance, area, and shape on the accuracy of reconstruction will be examined. The efficiency of reconstruction using the HELS method as the increase in frequency will also be studied. [Work supported by the NSF, Grant No. CMS-9802847.]