An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges
An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/286710 |
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| _version_ | 1832562232797429760 |
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| author | Xue Kai Wang Jiufa Li Qiuhong Wang Weiyuan Wang Ping |
| author_facet | Xue Kai Wang Jiufa Li Qiuhong Wang Weiyuan Wang Ping |
| author_sort | Xue Kai |
| collection | DOAJ |
| description | An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method. |
| format | Article |
| id | doaj-art-fe3bdb4483474e07905071d54f2de56e |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-fe3bdb4483474e07905071d54f2de56e2025-02-03T01:23:09ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/286710286710An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained EdgesXue Kai0Wang Jiufa1Li Qiuhong2Wang Weiyuan3Wang Ping4College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, ChinaAn analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.http://dx.doi.org/10.1155/2014/286710 |
| spellingShingle | Xue Kai Wang Jiufa Li Qiuhong Wang Weiyuan Wang Ping An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges Shock and Vibration |
| title | An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges |
| title_full | An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges |
| title_fullStr | An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges |
| title_full_unstemmed | An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges |
| title_short | An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges |
| title_sort | exact series solution for the vibration of mindlin rectangular plates with elastically restrained edges |
| url | http://dx.doi.org/10.1155/2014/286710 |
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