This content is not included in
your SAE MOBILUS subscription, or you are not logged in.
A New Technique Combining Eigenfunction Expansions and Boundary Elements to Solve Acoustic Radiation Problems
Technical Paper
2005-01-2504
ISSN: 0148-7191, e-ISSN: 2688-3627
Annotation ability available
Sector:
Language:
English
Abstract
A central problem in noise control involves the calculation of sound radiation and the holographic reconstruction of sources. A standard method for such calculations employs boundary elements and the surface Helmholtz integral equation (SHIE). However, difficulties occur at frequencies for which a congruent pressure-release boundary would have interior resonances. In such cases the SHIE does not have a unique solution and the matrix used in the boundary element method is singular. This talk will present a new technique which employs both eigenfunction expansions (typically using spherical wavefunctions) and boundary element matrices. This new method avoids problems with internal resonances and singular matrices, does not require adding internal “CHIEF” points, and permits fast and accurate holographic reconstructions for arbitrarily shaped sources. Advantageous operations termed “iterative deepening”, which automatically discards unnecessary eigenfunctions and detects any symmetries in the problem, and “forward refinement” with “parametric relaxation”, which guarantees convergence to a correct and accurate solution, will be presented. Application of this new method to inverse propagation will be discussed.
Recommended Content
Technical Paper | Noise Problems Associated with Geometrically Stiffened Panels |
Technical Paper | The Reduction of Air-Rush Noise in Plastic Engine Intake Manifolds |
Technical Paper | Transient Tyre Noise Measurements Using Time Domain Acoustical Holography |
Authors
Citation
Maynard, J., "A New Technique Combining Eigenfunction Expansions and Boundary Elements to Solve Acoustic Radiation Problems," SAE Technical Paper 2005-01-2504, 2005, https://doi.org/10.4271/2005-01-2504.Also In
References
- Wu T. W. Boundary Element Acoustics: Fundamentals and Computer Codes WIT Press South Hampton, Boston 2000
- Amini S. Ke Chen Harris P. J. “Iterative solutions of boundary value equations for the exterior Helmholtz problem,” J. Sound Vib. 112 257 262 1990
- Marburg Steffen Scheider Stefan Hardtke Has-Juergen “Iterative solution techniques for boundary element method (BEM) equations,” J. Acoust Soc. Am. 112 2381 2002 Marburg Steffen Schneider Stefan “Performance of iterative solvers for acoustic problems,”
- Morse Philip M. Herman Feshbach Methods of Theoretical Physics McGraw-Hill New York 1953
- Williams W. Parke N. G. Moran D. A. Sherman Charles H. “Acoustic radiation from a finite cylinder,” J. Acoust. Soc. Am. 36 2316 2322 1964
- Chao Y-C. “An implicit least-squares method for the inverse problem of acoustic radiation,” J. Acoust. Soc. Am. 81 1288 1292 1987
- Maynard J. D. “Nearfield acoustic holography and arbitrarily shaped sources,” International Meeting on Acoustical Imaging J. Imagerie Acoustique SFA, GAIE Lyon, France 1994 25 28
- Maynard J. D. “Nearfield acoustic holography: a review,” Proceedings of InterNoise 2001 2001
- Schenk H. A. “Improved integral formulation for acoustic radiation problems,” J. Acoust. Soc. Am. 44 41 58 1968
- Burton A. J. Miller G. F. “The application of internal equation methods to the numerical solution of some exterior boundary-value problems,” Proc. Roy. Soc. Lond. A 323 201 210 1971
- Press W. H. Teukolsky S. A. Vettering W. T. Flannery B. P. Numerical Recipes Cambridge University Press Cambridge 1992
- Koopmann G. H. Song L. Fahnline J. B. “A method for computing acoustic fields based on the principle of wave superposition,” J. Acoust. Soc. Amer. 86 2433 1989
- Huang Y. Computer Techniques for Three-Dimensional Source Radiation The Pennsylvania State University 1990
- Wang Z. Wu S. F. “Helmholtz equation-least-squares method for reconstructing the acoustic pressure field,” J. Acoust. Soc. Am. 91 2020 2032 1997
- Isakov V. Wu S. F. “On theory and application of HELS method in inverse acoustics,” Inverse Problem 18 1147 1159 2002
- Chess Skill in Man and Machine Frey Peter W. Springer Verlag New York 1978