A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners
It is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, wh...
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| Format: | Article |
| Language: | English |
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Elsevier
2016-06-01
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| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S209044791500091X |
| _version_ | 1819087743050842112 |
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| author | S.A. Eftekhari |
| author_facet | S.A. Eftekhari |
| author_sort | S.A. Eftekhari |
| collection | DOAJ |
| description | It is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance. |
| first_indexed | 2024-12-21T21:40:59Z |
| format | Article |
| id | doaj.art-caa6c3f3a678417ea0e4557dbf0a7fe6 |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-21T21:40:59Z |
| publishDate | 2016-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-caa6c3f3a678417ea0e4557dbf0a7fe62022-12-21T18:49:22ZengElsevierAin Shams Engineering Journal2090-44792016-06-017277779010.1016/j.asej.2015.05.016A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free cornersS.A. EftekhariIt is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance.http://www.sciencedirect.com/science/article/pii/S209044791500091XMixed Ritz-DQM approachRectangular platesBoundary conditionsFree corners |
| spellingShingle | S.A. Eftekhari A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners Ain Shams Engineering Journal Mixed Ritz-DQM approach Rectangular plates Boundary conditions Free corners |
| title | A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners |
| title_full | A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners |
| title_fullStr | A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners |
| title_full_unstemmed | A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners |
| title_short | A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners |
| title_sort | simple and accurate mixed ritz dqm formulation for free vibration of rectangular plates involving free corners |
| topic | Mixed Ritz-DQM approach Rectangular plates Boundary conditions Free corners |
| url | http://www.sciencedirect.com/science/article/pii/S209044791500091X |
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