Local High-Order Radiation Boundary Conditions For The Two-Dimensional Time-Dependent Structural Acoustics Problem

Journal of the Acoustical Society of America

Volumn 91, Issue 3, 1992, Pages 1320-1335

  Pinsky, Peter M ^a   Thompson, Lonny L ^a   Abboud, Najib N ^b  

^a STANFORD UNIVERSITY   (United States)

^b WEIDLINGER ASSOCIATES INC   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTICS; ARTICLE; BIOPHYSICS; FOURIER TRANSFORMATION; MATHEMATICAL ANALYSIS; RADIATION;

EID: 0026749979     PISSN: 00014966     EISSN: NA     Source Type: Journal    
DOI: 10.1121/1.402461     Document Type: Article

References (55)

1. M. C. Junger, “Radiation and scattering by submerged elastic structures, “ J. Acoust. Soc. Am. 57, 1318-1326 (1975).
2. M. C. Junger and D. Feit, Sound, Structures and Their Interaction (M.I.T. Press, Cambridge, MA, 1986), 2nd ed.
3. D. G. Crighton, “The 1988 Rayleigh medal lecture: Fluid loading-The interaction between sound and vibration, “ J. Sound Vib. 133, 1-27 (1989).
4. J. B. Mariem and M. A. Hamdi, “A new boundary finite element method for fluid-structure interaction problems, “ Int. J. Num. Methods Eng. 24, 1251-1267(1987).
5. G. C. Everstine and F. M. Henderson, “Coupled finite element/boundary element approach for fluid-structure interaction, “ J. Acoust. Soc. Am. 87, 1938-1947(1990).
6. R. A. Jeans and I. C. Mathews, “Solution of fluid-structure interaction problems using a coupled finite element and variational boundary element technique, “ J. Acoust. Soc. Am. 88, 2459-2466 (1990).
7. C. M. Piaszczyk and J. M. Klosner, “Acoustic radiation from vibrating surfaces at characteristic frequencies, “ J. Acoust. Soc. Am. 75, 363-375 (1984).
8. L. G. Copley, “Fundamental results concerning integral representations in acoustic radiation, “ J. Acoust. Soc. Am. 44, 28-32 (1968).
9. H. A. Schenck, “Improved integral formulation for acoustic radiation problems, “ J. Acoust. Soc. Am. 44, 41-58 (1968).
10. A. J. Burton and G. F. Miller, “The application of integral equation methods to the numerical solution of some exterior boundary value problems, “ Proc. R. Soc. London. Ser. A 323, 201-210 (1971).
11. I.C. Mathews, “Numerical techniques for three-dimensional steady-state fluid-structure interaction, “ J. Acoust. Soc. Am. 79, 1317-1325 (1986).
12. S. Amini and P. J. Harris, “A comparison between various boundary integral formulations of the exterior acoustic problem, “ Comput. Methods Appl. Mech. Eng. 84, 59-75 (1990).
13. D. Givoli and J. B. Keller, “A finite element method for large domains, “ Comput. Methods Appl. Mech. Eng. 76, 41-66 (1989).
14. J. B. Keller, and D. Givoli, “Exact nonreflecting boundary conditions, “ J. Comput. Phys. 82, 172-192 (1989).
15. I. Harari and T. J. R. Hughes, “Finite element methods for the Helmholtz equation in an exterior domain: Model problems, “ Comput. Methods Appl. Mech. Eng. 87, 59-96 (1991).
16. O. C. Zienkiewicz and P. Bettess, “Fluid-structure dynamic interaction and wave forces. An introduction to numerical treatment, “ Int. J. Num. Methods Eng. 13, 1-16 (1978).
17. N. N. Abboud, “A mixed finite element formulation for the transient and harmonic exterior fluid-structure interaction problem, “ Ph.D. thesis, Stanford University, August 1990.
18. D. Givoli, “Non-reflecting boundary conditions: A review, “ J. Comput. Phys. 94, 1-29(1991).
19. G. D. Manolis, “A comparitive study on three boundary element method approaches to problems in elastodynamics, “ Int. J. Num. Methods Eng. 19, 73-91 (1983).
20. R. P. Shaw, “Boundary integral equation methods applied to wave problems, “ in Developments in Boundary Element Methods, edited by P. Ban-erjee and S. Mukherjee, London, 1984, Applied Science, Vol. 3, Chap. 6.
21. W. J. Mansur and C. A. Brebbia, “Formulation of the boundary element method for transient problems governed by the scalar wave equation, “ Appl. Math. Modelling, 6, 307-311 (1982).
22. W. J. Mansur and C. A. Brebbia, “Further developments on the solution of the transient scalar wave equation, “ in Topics in Boundary Element Research, edited by C. A. Brebbia (Springer-Verlag, Berlin, 1984), Vol. 2.
23. H. Huang, G. C. Everstine, and Y. F. Wang, “Retarded potential techniques for the analysis of submerged structures impinged by weak shock waves, “ in Computational Methods for Fluid-Structure Interaction Problems, edited by T. Bely tschko and T. L. Geers (ASME, New York, 1977), Vol. AMD 26, pp. 83-93.
24. Y. P. Lu, “The application of retarded potential techniques to submerged dynamic structural systems, “ Proceedings of the 2nd International Symposium Innovative Numerical Analysis for the Applied Engineering Sciences, edited by R. P. Shaw and W. Pilkey, 1980, pp. 59-68.
25. D. Givoli, A Finite Element Method for Large Domain Problems, Ph.D. thesis, Stanford University, May 1988.
26. O. C. Zienkiewicz and R. E. Newton, “Coupled vibrations of a structure submerged in a compressible fluid, “ in International Symposium on Finite Element Techniques (Univ. Stutgardt, Germany, 1969).
27. O. C. Zienkiewicz, D. W. Kelley, and P. Bettess, “The Sommerfeld (radiation) condition on infinite domains and its modelling in numerical procedures, “ in the 3rd International Symposium Computational Methods and Applied Science Engineering (IRIA Laboria, Versailles, France, 1977).
28. T. L. Geers, “Residual potential and approximate methods for three-dimensional fluid-structure interaction problem, “ J. Acoust. Soc. Am. 49, 1505-1510(1971).
29. C. A. Felippa, “Top-down derivation of doubly asymptotic approximation for fluid-structure interaction analysis, “ in Innovative Numerical Analysis for the Applied Engineering Sciences, (U. P. of Virginia, City, 1980), Vol. 46, pp. 79-88.
30. B. Nicolas Vullierme, “A contribution to doubly asymptotic approximations: An operator top-down derivation, “ in Numerical Technology in Acoustic Radiation (ASME, New York, 1989), Vol. 6, pp. 7-13.
31. H. C. Neilson, G. C. Everstine, and Y. F. Wang, “Transient response of a submerged fluid-coupled double-walled shell structure to a pressure pulse, “ J. Acoust. Soc. Am. 70, 1776-1782 (1981).
32. C. A. Felippa and J. A. Deruntz, “Finite element analysis of shock-induced hull cavitation, “ Comput. Methods Appl. Mech. Eng. 44,297-337 (1984).
33. G. C. Ruzicka and T. L. Geers, “Transient response analysis of multiple-submerged structures, “ Finite Elements Anal. Design, 153-172 (1989).
34. B. Engquist and A. Majda, “Absorbing boundary conditions for the numerical simulation of waves, “ Math. Comput. 31, 629-652 (1977).
35. B. Engquist and A. Majda, “Radiation boundary conditions for acoustic and elastic calculations, “ Commun. Pure Appl. Math. 32, 313-357 (1979).
36. A. Bayliss and E. Turkel, “Radiation boundary conditions for wave-like equations, “ Commun. Pure Appl. Math. XXXIII, 707-725 (1980).
37. A. Bayliss, M. Gunzburger, and E. Turkel, “Boundary conditions for the numerical solution of elliptic equations in exterior regions, “ SIAM J. Appl. Math. 42, 430-451 (1982).
38. P. M. Pinsky and N. N. Abboud, “Transient finite element analysis of the exterior structural acoustics problem, “ ASME J. Vib. Acoust. 112, 245-256(1990).
39. P. M. Pinsky and N. N. Abboud, “Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic boundary operators, “ Comput. Methods Appl. Mech. Eng. 85, 311-348 (1991).
40. K. Bando, P. Bettess, and C. Emson, “The effectiveness of dampers for the analysis of exterior scalar wave diffraction by cylinders and ellipsoids, “ Int. J. Num. Methods Fluids, 4, 599-617 (1984).
41. K. J. Bathe and W. Hahn, “On transient analysis of fluid-structure systems, “ Comput. Struct. 10, 383-391 (1979).
42. T. B. Belytschko, “Fluid-structure interaction, “ Comput. Struct. 12, 459-469(1980).
43. G. C. Everstine, “A symmetric potential formulation for fluid-structure interaction, “ J. Sound Vib. 79, 157-160 (1981).
44. G. M. L. Gladwell, “A variational formulation of damped acousto-struc-tural vibration problems, “ J. Sound Vib. 4, 172-186 (1966).
45. A. Craggs, “The transient response of a coupled plate-acoustic system using plate and acoustic finite elements, “ J. Sound Vib. 15, 509-528 (1971).
46. A. Sommerfeld, Partial Differential Equations in Physics (Academic, New York, 1964).
47. P. M. Morse and K. U. Ingard, Theoretical Acoustics (McGraw-Hill, New York, 1968).
48. G. N. Watson, Theory of Bessel Functions (Cambridge U.P., Cambridge, 1966).
49. S. N. Karp, “A convergent farfield expansion for two-dimensional radiation functions, “ Commun. Pure Appl. Math. XIV, 427-434 (1961).
50. T. J. R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1987).
51. N. N. Abboud and P. M. Pinsky, “Finite element solution and dispersion analysis for the transient structural acoustics problem, “ Appl. Mech. Rev., 43 (1990) (supplement).
52. E. Dokumaci, “A study of the failure of numerical solutions in boundary element analysis of acoustic radiation problems, “ J. Sound Vib. 139, 83-97(1990).
53. M. C. Junger, “Vibrations of elastic shells in a fluid medium and the associated radiation of sound, “ J. Appl. Mech. 19, 439-445 (1952).
54. H. H. Bleich and M. L. Baron, “Free and forced vibrations of an infinitely long cylindrical shell in an infinite acoustic medium, “ J. Appl. Mech. 21, 167-177(1954).
55. L. Cremer, M. Heckl, and E. Ungar, Structure-Borne Sound (Springer-Verlag, Berlin, 1988), 2nd ed.