The complex equivalent source method for sound propagation over an impedance plane

Journal of the Acoustical Society of America

Volumn 116, Issue 6, 2004, Pages 3304-3311

  Ochmann, Martin ^a  

^a BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC IMPEDANCE; BOUNDARY ELEMENT METHOD; GREEN'S FUNCTION; HEAT CONDUCTION; INTEGRAL EQUATIONS; MIRRORS; REFLECTION;

HALF-SPACE PROBLEMS; HANKEL FUNCTION; SUPERPOSITION; SURFACE IMPEDANCE; WAVE NUMBER;

ACOUSTIC WAVE PROPAGATION;

ACOUSTIC IMPEDANCE; ARTICLE; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; SOUND; SOUND TRANSMISSION; VALIDATION PROCESS;

EID: 11144275846     PISSN: 00014966     EISSN: None     Source Type: Journal    
DOI: 10.1121/1.1819504     Document Type: Article

References (33)

1. A. Sommerfeld, "Über die Ausbreitung der Wellen in der drahtlosen Telegraphie," ("The propagation of waves in wireless telegraphy"), Ann. Phys. (Leipzig) 28, 665-736 (1909).
2. A. Sommerfeld, "Über die Ausbreitung der Wellen in der drahtlosen Telegraphie" ("The propagation of waves in wireless telegraphy"), Ann. Phys. (Leipzig) 81, 1135-1153 (1926).
3. A. Sommerfeld, Partielle Differentialgleichungen der Physik (Partial Differential Equations in Physics) (Harri Deutsch, Thun-Frankfurt/M, 1978).
4. K. Attenborough, "Sound propagation close to the ground," Annu. Rev. Fluid Mech. 34, 51-82 (2002).
5. F. P. Mechel, Schallabsorber Band. I, Sound Absorbers Vol. I (Hirzel, Stuttgart, 1989), Chap. 13, pp. 513-666.
6. T. F. W. Embleton, "Tutorial on sound propagation outdoors," J. Acoust. Soc. Am. 100, 31-48 (1996).
7. Boundary Element Acoustics: Fundamentals and Computer Codes, Advances in Boundary Element Series, edited by T. W. Wu (WIT, Computational Mechanics, Southampton, Boston, 2000).
8. Boundary Elements in Acoustics, Advances and Applications, Advances in Boundary Element Series, edited by O. von Estorff (WIT, Computational Mechanics, Southampton, Boston, 2000).
9. A. F. Seybert and B. Soenarko, "Radiation and scattering of acoustic waves from bodies of arbitrary shape in a three-dimensional half space," ASME J. Vib., Acoust., Stress, Reliab. Des. 110, 112-117 (1988).
10. W. L. Li, T. W. Wu, and A. F. Seybert, "A half-space boundary element method for acoustic problems with a reflecting plane of arbitrary impedance," J. Sound Vib. 171, 173-184 (1994).
11. L. A. de Lacerda, L. C. Wrobel, H. Power, and W. J. Mansur, "A novel boundary integral formulation for three-dimensional analysis of thin acoustics barriers over an impedance plane," J. Acoust. Soc. Am. 104, 671-678 (1998).
12. C. Granat, M. Ben Tahar, and T. Ha-Duong, "Variational formulation using integral equations to solve sound scattering above an absorbing plane," J. Acoust. Soc. Am. 105, 2557-2564 (1999).
13. M. Ochmann, "The source simulation technique for acoustic radiation problems," Acustica 81, 512-527 (1995).
14. M. Ochmann, "The full-field equations for acoustic radiation and scattering," J. Acoust. Soc. Am. 105, 2574-2584 (1999).
15. Y. L. Li and M. J. White, "Near-field computation for sound propagation above ground-using complex image theory," J. Acoust. Soc. Am. 99, 755-760 (1996).
16. J. A. Fawcett, "Complex-image approximations to the half-space acoustoelastic Green's function," J. Acoust. Soc. Am. 108, 2791-2795 (2000).
17. J. A. Fawcett, "A method of images for a penetrable acoustic waveguide," J. Acoust. Soc. Am. 113, 194-204 (2003).
18. R. Raspet and G. E. Baird, "The acoustic surface wave above a complex impedance ground," J. Acoust. Soc. Am. 85, 638-640 (1989).
19. B. Davies, Integral Transforms and Their Applications, 3rd ed. (Springer, New York Berlin Heidelberg, 2002).
20. D. Habault and P. J. T. Filippi, "Ground effect analysis: Surface wave and layer potential representations," J. Sound Vib. 79, 529-550 (1981).
21. H. Brick, M. Ochmann, Eine BEM-Toolbox zur Berechnung der Schallabstrahlung schwingender Strukturen vor Hindernissen und über absorbierendem Boden ("A BEM-Toolbox for calculation of sound radiation from vibrating structures in front of barriers and above absorbing ground"), on CD-ROM: Aachen DAGA 2003, Fortschritte der Akustik (ISBN 3-9808659-0-8), available from Deutsche Gesellschaft für Akustik, Fachbereich Physik, Universitaet Oldenburg, 26111 Oldenburg, Germany), 542-543, 2003.
22. C. F. Gauss, Disquisitiones Arithmeticae (Lispiae in commissis apud Gerh. Fleischer Iun. 1801; German translation by H. Maser (Chelsea, New York, 1965), Art. 55.
23. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed. (Springer, Berlin Heidelberg New York, 1966), Sec. 3.6.2, p. 82.
24. G. A. Deschamps, "Gaussian beams as a bundle of complex rays," Electron. Lett. 7, 684-685 (1971).
25. L. B. Felsen, "Complex-source-point-solutions of the field equations and their relation to the propagation and scattering of Gaussian beams," in Instituto Nazionale di Alta Matematica, Symposia Matematica (Academic, London, 1976), 18, pp. 40-56 (1976).
26. L. B. Felsen, "Evanescent waves," J. Opt. Soc. Am. 66, 751-760 (1976).
27. E. Heyman and L. B. Felsen, "Complex-source pulsed-beam fields," J. Opt. Soc. Am. A 6, 806-817 (1989).
28. R. W. Ziolkowski, "Exact solutions of the wave equation with complex source locations," J. Math. Phys. 26, 861-863 (1985).
29. M. A. Nobile and S. I. Hayek, "Acoustic propagation over an impedance plane," J. Acoust. Soc. Am. 78, 1325-1336 (1985).
30. I. V. Lindell and E. Alanen, "Exact image theory for the Sommerfeld half-space problem," IEEE Trans. Antennas Propag. 32, Part I: Vertical magnetic dipole, 32, 126-133 (1984); Part II: Vertical electric dipole, 32, 841-847 (1984); Part III: General formulation, 32, 1027-1032 (1984).
31. I. V. Lindell and E. Alanen, "Exact image theory for the Sommerfeld half-space problem," IEEE Trans. Antennas Propag. 32, Part I: Vertical magnetic dipole, 32, 126-133 (1984); Part II: Vertical electric dipole, 32, 841-847 (1984); Part III: General formulation, 32, 1027-1032 (1984).
32. I. V. Lindell and E. Alanen, "Exact image theory for the Sommerfeld half-space problem," IEEE Trans. Antennas Propag. 32, Part I: Vertical magnetic dipole, 32, 126-133 (1984); Part II: Vertical electric dipole, 32, 841-847 (1984); Part III: General formulation, 32, 1027-1032 (1984).
33. I. V. Lindell and E. Alanen, "Exact image theory for the Sommerfeld half-space problem," IEEE Trans. Antennas Propag. 32, Part I: Vertical magnetic dipole, 32, 126-133 (1984); Part II: Vertical electric dipole, 32, 841-847 (1984); Part III: General formulation, 32, 1027-1032 (1984).