Acoustic eigenanalysis for multiply-connected problems using dual BEM

Communications in Numerical Methods in Engineering

Volumn 20, Issue 6, 2004, Pages 419-440

  Chen, J T ^a   Liu, L W ^a   Chyuan, S W ^b  

^a NATIONAL TAIWAN OCEAN UNIVERSITY   (Taiwan)

^b CHUNG SHAN INSTITUTE OF SCIENCE AND TECHNOLOGY   (Taiwan)

Author keywords

Boundary element method; CHIEF concept; Fredholm alternative theorem; Multiply connected domain; Singular value decomposition

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS;

ACOUSTIC EIGNANALYSIS; EIGENMODES; NULL-FIELD EQUATION;

EIGENVALUES AND EIGENFUNCTIONS;

BOUNDARY ELEMENT METHOD; EIGENVALUE;

EID: 2642549816     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/cnm.679     Document Type: Article

References (27)

1. Partridge PW, Brebbia CA, Wrobel LC. The Dual Reciprocity Boundary Element Method. Computational Mechanics Publications: Southampton, 1992.
2. Nowak AJ, Neves AC (eds). Multiple Reciprocity Boundary Element Method. Computational Mechanics Publications: Southampton, 1994.
3. Itagaki M, Nishiyama S, Tomioka S, Enoto T, Sahashi N. Power iterative multiple reciprocity boundary element method for solving three-dimensional Helmholtz equation. Engineering Analysis with Boundary Elements 1997; 20:113-121.
4. Kamiya N, Andoh E, Nogae K. A new complex-valued formulation and eigenvalue analysis of the Helmholtz equation by boundary element method. Advances in Engineering Software 1996; 26:219-227.
5. Tai GRG, Shaw RP. Helmholtz equation eigenvalues and eigenmodes for arbitrary domains. Journal of the Acoustical Society of America 1974; 56:796-804.
6. De Mey G. Calculation of the Helmholtz equation by an integral equation. International Journal for Numerical Methods in Engineering 1976; 10:59-66.
7. De Mey G. A simplified integral equation method for the calculation of the eigenvalues of Helmholtz equation. International Journal for Numerical Methods in Engineering 1977; 11:1340-1342.
8. Hutchinson JR. An alternative BEM formulation applied to membrane vibrations. In Boundary Elements VII, Brebbia CA, Maier G (ed.). Springer: Berlin, 1985.
9. Chen JT, Huang CX, Wong FC. Determination of spurious eigenvalues and multiplicities of true eigenvalues in the dual multiple reciprocity method using the singular value decomposition technique. Journal of Sound and Vibration 2000; 230:219-230.
10. Kuo SR, Chen JT, Huang CX. Analytical study and numerical experiments for true and spurious eigensolutions of a circular cavity using the real-part dual BEM. International Journal for Numerical Methods in Engineering 2000; 48:1404-1422.
11. Berry MW, Drmac Z, Jessup ER. Matrices, vector spaces, and information retrieval. SIAM Review 1999; 41: 335-362.
12. Golub GH, Van Loan CF. Matrix Computations (2nd edn). The Johns Hopkins University Press: Baltimore, 1989.
13. Kuo SR, Yeih W, Wu YC. Applications of the generalized singular-value decomposition method on the eigenproblem using the incomplete boundary element formulation. Journal of Sound and Vibration 2000; 235:813-845.
14. Chen IL, Chen JT, Kuo SR, Liang MT. A new method for true and spurious eigensolutions of arbitrary cavities using the CHEEF method. Journal of the Acoustical Society of America 2001; 109:982-999.
15. Schenck HA. Improved integral formulation for acoustic radiation problem. Journal of the Acoustical Society of America 1968; 44:41-58.
16. Seybert AF, Rengarajan TK. The use of CHIEF to obtain unique solutions for acoustic radiation using boundary integral equations. Journal of the Acoustical Society of America 1987; 81:1299-1306.
17. Chen JT, Lin JH, Kuo SR, Chyuan SW. Boundary element analysis for the Helmholtz eigenvalue problems with a multiply connected domain. Proceedings of the Royal Society of London Series A 2001; 457:2521-2546.
18. Kitahara M. Boundary Integral Equation Methods in Eigenvalue Problems of Elastodynamics and Thin Plates. Elsevier: Amsterdam, 1985.
19. Burton AJ, Miller GF. The application of integral equation methods to numerical solution of some exterior boundary value problems. Proceedings of the Royal Society of London Series A 1971; 323:201-210.
20. Chen JT, Liu LW, Hong H-K. Spurious and true eigensolutions of Helmholtz BIEs and BEMs for a multiply connected problem. Proceedings of the Royal Society of London Series A 2003; 459:1841-1924.
21. Lin WH. Guided waves in a circular duct containing an assembly of circular cylinders. Journal of Sound and Vibration 1981; 79:463-477.
22. Nagaya K, Poltorak K. Method for solving eigenvalue problems of the Helmholtz equation with a circular outer and a number of eccentric circular inner boundaries. Journal of the Acoustical Society of America 1989; 85: 576-581.
23. Nagaya K, Yamaguchi T. Method for solving eigenvalue problems of the Helmholtz equation with a arbitrarily shaped outer and a number of eccentric circular inner boundaries. Journal of the Acoustical Society of America 1991; 90:2146-2153.
24. Chen JT, Chen KH. Dual integral formulation for determining the acoustic modes of a two-dimensional cavity with a degenerate boundary. Engineering Analysis with Boundary Elements 1998; 21:105-116.
25. Chen JT, Hong H-K. Review of dual boundary element methods with emphasis on hypersingular integral and divergent series. Applied Mechanics Reviews 1999; 52:17-33.
26. Matrin PA. On the null-field equations for the exterior problems of acoustics. Quarterly Journal of Mechanics and Applied Mathematics 1980; 27:386-396.
27. Chen JT, Kuo SR, Lin JH. Analytical study and numerical experical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticity. International Journal for Numerical Methods in Engineering 2002, 54:1669-1681.