Abstract:
We analyze a quadratic eigenvalue problem related to the damped vibrations of an acoustic fluid in a cavity with absorbing walls. The problem is shown to be equivalent to the spectral problem for a non-compact operator and a thorough spectral characterization is given. We consider a discretization based on Raviart-Thomas finite elements and show that it is free of spurious modes and convergent with optimal order. Numerical results for a test case with known exact analytical solution are also included.
Registro:
| Documento: |
Conferencia
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| Título: | A finite element method to compute damped vibration modes in dissipative acoustics |
| Autor: | Bermúdez, A.; Durán, R.G.; Rodríguez, R.; Solomin, J.; Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona |
| Ciudad: | Barcelona |
| Filiación: | Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706, Santiago de Compostela, Spain
Departamento de Matemática, Facultad de Ciencias Exactas Y Naturales, Universidad de Buenos Aires, 1428 - Buenos Aires, Argentina
Departamento de Ingeniería Matemática, Universidad de Concepcíon, Casilla 160-C, Concepción, Chile
Departamento de Mateḿatica, Facultad de Ciencias Exactas, Universidad Nacional de la Plata, C.C. 172, 1900 - La Plata, Argentina
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| Palabras clave: | Dissipative acoustics; Finite element spectral approximation; Quadratic eigenvalue problems; Damped vibrations; Dissipative acoustics; Exact analytical solutions; Numerical results; Quadratic eigenvalue problems; Raviart-Thomas finite elements; Spectral approximations; Spectral characterization; Computational methods; Spectrum analyzers; Eigenvalues and eigenfunctions |
| Año: | 2000
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| Título revista: | European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
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| Título revista abreviado: | Eur. Congr. Comput. Methods Appl. Sci. Eng., ECCOMAS
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez |
Referencias:
- Bermudez, A., Duran, R., Muschietti, M.A., Rodriguez, R., Solomin, J., Finite element vibration analysis of fluid-solid systems without spurious modes (1995) SIAM J. Numer. Anal, 32, pp. 1280-1295
- Bermudez, A., Duran, R., Rodriguez, R., Solomin, J., Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics SIAM J. Numer. Anal, , to appear
- Bermudez, A., Hervella-Nieto, L., Rodriguez, R., Finite element computation of three-dimensional elastoacustic vibrations (1999) J. Sound Vibr, 219, pp. 277-304
- Bermudez, A., Hervella-Nieto, L., Rodriguez, R., Finite element computation of the vibrations of a plate-fluid system with interface damping (1998) Technical Report DIM 98-25, , Universidad de Concepcion
- Bermudez, A., Rodriguez, R., Finite element computation of the vibration modes of a fluid-solid system (1994) Comp. Methods Appl. Mech. Engng, 119, pp. 355-370
- Bermudez, A., Rodriguez, R., Numerical computation of elastoacoustic vibrations with interface damping (1998) Equations Aux Derivees Partielles Et Applications, pp. 165-187. , Gauthier-Villars
- Bermudez, A., Rodriguez, R., Modeling and numerical solution of elastoacoustic vibrations with interface damping (1999) Int. J. Numer. Methods Engng., 46, pp. 1763-1779
- Brezzi, F., Fortin, M., (1991) Mixed and Hybrid Finite Element Methods, , Springer-Verlag
- Descloux, J., Nassif, N., Rappaz, J., On spectral approximation Part 1: The problem of convergence (1978) R.A.I.R.O. Anal. Numer, 12, pp. 97-112
- Descloux, J., Nassif, N., Rappaz, J., On spectral approximation Part 2:e rror estimates for the galerkin method (1978) R.A.I.R.O. Anal. Numer, 12, pp. 113-119
- Girault, V., Raviart, P.A., (1986) Finite Element Methods for Navier-Stokes Equations, , Springer-Verlag
- Hamdi, M., Ouset, Y., Verchery, G., A displacement method for the analysis of vibrations of coupled fluid-structure systems (1978) Int. J. Numer. Methods Engng, 13, pp. 139-150
- Kehr-Kandille, V., Ohayon, R., Elastoacoustic damped vibrations Finite element and modal reduction methods (1992) New Advances in Computational Structural Mechanics, pp. 321-334. , O.C. Zienkiewicz and P. Ladeveze, eds. Elsevier
- Krein, M.G., Langer, H., On some mathematical principles in the linear theory of damped oscillations of continua I (1978) Integ. Eqns. Oper. Theory, 1-3, pp. 364-399
- Raviart, P.A., Thomas, J.M., A mixed finite element method for second order elliptic problems (1977) Mathematical Aspects of Finite Element Methods, pp. 292-315. , Lecture Notes in Mathematics 606, Springer-Verlag
- Rodriguez, R., Solomin, J., The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems (1996) Math. Comp, 65, pp. 1463-1475A4 - Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona
Citas:
---------- APA ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J. & Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona
(2000)
. A finite element method to compute damped vibration modes in dissipative acoustics. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez [ ]
---------- CHICAGO ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J., Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona
"A finite element method to compute damped vibration modes in dissipative acoustics"
. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000
(2000).
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez [ ]
---------- MLA ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J., Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona
"A finite element method to compute damped vibration modes in dissipative acoustics"
. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, 2000.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez [ ]
---------- VANCOUVER ----------
Bermúdez, A., Durán, R.G., Rodríguez, R., Solomin, J., Commission of European Communities (EC); Ministerio de Ciencia y Tecnologia; Generalitat de Catalunya, Comissio Interdepartamental; de Recerca i Innovacio Tecnologica (CIRIT); Autoritat Portuaria de Barcelona A finite element method to compute damped vibration modes in dissipative acoustics. Eur. Congr. Comput. Methods Appl. Sci. Eng., ECCOMAS. 2000.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez [ ]
