Axisymmetric Natural Frequencies of Statically Loaded Annular Plates
We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations o...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2003/715675 |
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| _version_ | 1832555555787374592 |
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| author | Eihab M. Abdel-Rahman Waleed F. Faris Ali H. Nayfeh |
| author_facet | Eihab M. Abdel-Rahman Waleed F. Faris Ali H. Nayfeh |
| author_sort | Eihab M. Abdel-Rahman |
| collection | DOAJ |
| description | We present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies. |
| format | Article |
| id | doaj-art-ac092fe445924bdf80433b0776e5af4c |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-ac092fe445924bdf80433b0776e5af4c2025-02-03T05:47:52ZengWileyShock and Vibration1070-96221875-92032003-01-01105-630131210.1155/2003/715675Axisymmetric Natural Frequencies of Statically Loaded Annular PlatesEihab M. Abdel-Rahman0Waleed F. Faris1Ali H. Nayfeh2Department of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USADepartment of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USADepartment of Engineering Science and Mechanics, MC 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USAWe present a numerical procedure to solve the axisymmetric vibration problem of statically loaded annular plates. We use the von Kármán nonlinear plate model to account for large deformations and study the effect of static deflections on the natural frequencies and mode shapes for six combinations of boundary conditions. The shooting method is used to solve the resulting eigenvalue problem. Our results show that static deformations have a significant effect on the natural frequencies and small effect on the mode shapes of the plate. Further, the results show that the presence of in-plane stresses has a significant effect on the natural frequencies.http://dx.doi.org/10.1155/2003/715675 |
| spellingShingle | Eihab M. Abdel-Rahman Waleed F. Faris Ali H. Nayfeh Axisymmetric Natural Frequencies of Statically Loaded Annular Plates Shock and Vibration |
| title | Axisymmetric Natural Frequencies of Statically Loaded Annular Plates |
| title_full | Axisymmetric Natural Frequencies of Statically Loaded Annular Plates |
| title_fullStr | Axisymmetric Natural Frequencies of Statically Loaded Annular Plates |
| title_full_unstemmed | Axisymmetric Natural Frequencies of Statically Loaded Annular Plates |
| title_short | Axisymmetric Natural Frequencies of Statically Loaded Annular Plates |
| title_sort | axisymmetric natural frequencies of statically loaded annular plates |
| url | http://dx.doi.org/10.1155/2003/715675 |
| work_keys_str_mv | AT eihabmabdelrahman axisymmetricnaturalfrequenciesofstaticallyloadedannularplates AT waleedffaris axisymmetricnaturalfrequenciesofstaticallyloadedannularplates AT alihnayfeh axisymmetricnaturalfrequenciesofstaticallyloadedannularplates |