A finite element method to compute damped vibration modes in dissipative acoustics
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 b...
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2000
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez http://hdl.handle.net/20.500.12110/paper_84899257_v_n_p_Bermudez |
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paper:paper_84899257_v_n_p_Bermudez2023-06-08T16:36:50Z A finite element method to compute damped vibration modes in dissipative acoustics Duran, Ricardo Guillermo 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 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. Fil:Durán, R.G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez http://hdl.handle.net/20.500.12110/paper_84899257_v_n_p_Bermudez |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
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 |
| spellingShingle |
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 Duran, Ricardo Guillermo A finite element method to compute damped vibration modes in dissipative acoustics |
| topic_facet |
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 |
| description |
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. |
| author |
Duran, Ricardo Guillermo |
| author_facet |
Duran, Ricardo Guillermo |
| author_sort |
Duran, Ricardo Guillermo |
| title |
A finite element method to compute damped vibration modes in dissipative acoustics |
| title_short |
A finite element method to compute damped vibration modes in dissipative acoustics |
| title_full |
A finite element method to compute damped vibration modes in dissipative acoustics |
| title_fullStr |
A finite element method to compute damped vibration modes in dissipative acoustics |
| title_full_unstemmed |
A finite element method to compute damped vibration modes in dissipative acoustics |
| title_sort |
finite element method to compute damped vibration modes in dissipative acoustics |
| publishDate |
2000 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_84899257_v_n_p_Bermudez http://hdl.handle.net/20.500.12110/paper_84899257_v_n_p_Bermudez |
| work_keys_str_mv |
AT duranricardoguillermo afiniteelementmethodtocomputedampedvibrationmodesindissipativeacoustics AT duranricardoguillermo finiteelementmethodtocomputedampedvibrationmodesindissipativeacoustics |
| _version_ |
1768544202599170048 |