Lumped mass acoustic and membrane eigenanalysis using the global collocation method
The paper proposes a direct way to build lumped masses for performing eigenvalue analysis using the global collocation method in conjunction with tensor product Lagrange polynomials. Although the computational mesh is structured, it has a non-uniform density, in such a way that the internal nodes ar...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2014-12-01
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| Series: | Cogent Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23311916.2014.981366 |
| _version_ | 1797764556836044800 |
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| author | Christopher Provatidis |
| author_facet | Christopher Provatidis |
| author_sort | Christopher Provatidis |
| collection | DOAJ |
| description | The paper proposes a direct way to build lumped masses for performing eigenvalue analysis using the global collocation method in conjunction with tensor product Lagrange polynomials. Although the computational mesh is structured, it has a non-uniform density, in such a way that the internal nodes are located at the position of Gaussian points or the images of the roots of Chebyshev polynomials of second kind. As a result, the mass matrix degenerates to the identity matrix. In this particular nodal collocation procedure, no complex eigenvalue appears. The theory is successfully applied to rectangular and circular acoustic cavities and membranes. |
| first_indexed | 2024-03-12T19:57:27Z |
| format | Article |
| id | doaj.art-eae1e382d2d9479f9071b56d00394754 |
| institution | Directory Open Access Journal |
| issn | 2331-1916 |
| language | English |
| last_indexed | 2024-03-12T19:57:27Z |
| publishDate | 2014-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Cogent Engineering |
| spelling | doaj.art-eae1e382d2d9479f9071b56d003947542023-08-02T02:44:51ZengTaylor & Francis GroupCogent Engineering2331-19162014-12-011110.1080/23311916.2014.981366981366Lumped mass acoustic and membrane eigenanalysis using the global collocation methodChristopher Provatidis0National Technical University of AthensThe paper proposes a direct way to build lumped masses for performing eigenvalue analysis using the global collocation method in conjunction with tensor product Lagrange polynomials. Although the computational mesh is structured, it has a non-uniform density, in such a way that the internal nodes are located at the position of Gaussian points or the images of the roots of Chebyshev polynomials of second kind. As a result, the mass matrix degenerates to the identity matrix. In this particular nodal collocation procedure, no complex eigenvalue appears. The theory is successfully applied to rectangular and circular acoustic cavities and membranes.http://dx.doi.org/10.1080/23311916.2014.981366global collocationCAD/CAE integrationacousticsmembranes |
| spellingShingle | Christopher Provatidis Lumped mass acoustic and membrane eigenanalysis using the global collocation method Cogent Engineering global collocation CAD/CAE integration acoustics membranes |
| title | Lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| title_full | Lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| title_fullStr | Lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| title_full_unstemmed | Lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| title_short | Lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| title_sort | lumped mass acoustic and membrane eigenanalysis using the global collocation method |
| topic | global collocation CAD/CAE integration acoustics membranes |
| url | http://dx.doi.org/10.1080/23311916.2014.981366 |
| work_keys_str_mv | AT christopherprovatidis lumpedmassacousticandmembraneeigenanalysisusingtheglobalcollocationmethod |