3-D sound source reconstruction and field reprediction using the Helmholtz integral equation

Abstract A method for reconstruction of the boundary conditions of an arbitrarily shaped three-dimensional (3-D) sound source from a finite number of field pressures is presented and the associated field is repredicted by using the Helmholtz integral equation. To minimize the reconstruction error due to noise in the field pressures, a filtering method is proposed and it is verified that numerically singular values which correspond to the higher-order modes of the evanescent-like components of the source velocities are eliminated. For arbitrarily shaped sources with complex boundary conditions, the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source. Our technique can be used in computer-aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted.

[1]  F. Ursell,et al.  On the exterior problems of acoustics , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  A. Seybert,et al.  An advanced computational method for radiation and scattering of acoustic waves in three dimensions , 1985 .

[3]  Ben T. Zinn,et al.  Boundary integral solutions of three dimensional acoustic radiation problems , 1978 .

[4]  Yukio Kagawa,et al.  A finite element approach to a coupled structural-acoustic radiation system with application to loudspeaker characteristic calculation , 1980 .

[5]  H. A. Schenck.  Improved Integral Formulation for Acoustic Radiation Problems , 1968 .

[6]  W. Tabbara,et al.  Numerical aspects on coupling between complementary boundary value problems , 1973 .

[7]  G. F. Miller,et al.  The application of integral equation methods to the numerical solution of some exterior boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Earl G. Williams,et al.  Generalized nearfield acoustical holography for cylindrical geometry : theory and experiment , 1987 .

[9]  Ole J. Løkberg,et al.  ESPI—The ultimate holographic tool for vibration analysis? , 1982 .

[10]  D. Schweikert,et al.  Sound Radiation from an Arbitrary Body , 1963 .

[11]  Ole J. Lo kberg.  ESPI—The ultimate holographic tool for vibration analysis? , 1984 .

[12]  P.J.T. Filippi,et al.  Layer potentials and acoustic diffraction , 1977 .

[13]  T. K. Rengarajan,et al.  The use of CHIEF to obtain unique solutions for acoustic radiation using boundary‐integral equations , 1987 .

[14]  Tatsuo Yamabuchi,et al.  Acoustic Field in an Enclosure and Its Effect on Sound-Pressure Responses of a Loudspeaker , 1984 .

[15]  J. Lea,et al.  A finite element method for determining the acoustic modes of irregular shaped cavities , 1976 .

[16]  O. D. Kellogg.  Foundations of potential theory , 1934 .

[17]  J. D. Maynard,et al.  Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH , 1985 .

[18]  C. Piaszczyk,et al.  Acoustic radiation from vibrating surfaces at characteristic frequencies , 1984 .