A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges
A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the mi...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/8562079 |
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| _version_ | 1832564835504619520 |
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| author | Fuzhen Pang Haichao Li Yuan Du Shuo Li Hailong Chen Ning Liu |
| author_facet | Fuzhen Pang Haichao Li Yuan Du Shuo Li Hailong Chen Ning Liu |
| author_sort | Fuzhen Pang |
| collection | DOAJ |
| description | A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entire x-y plane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given. |
| format | Article |
| id | doaj-art-96e70e4e056545b9bd2105687395537a |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-96e70e4e056545b9bd2105687395537a2025-02-03T01:10:07ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/85620798562079A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the EdgesFuzhen Pang0Haichao Li1Yuan Du2Shuo Li3Hailong Chen4Ning Liu5College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaCollege of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, ChinaA series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entire x-y plane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given.http://dx.doi.org/10.1155/2018/8562079 |
| spellingShingle | Fuzhen Pang Haichao Li Yuan Du Shuo Li Hailong Chen Ning Liu A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges Shock and Vibration |
| title | A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges |
| title_full | A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges |
| title_fullStr | A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges |
| title_full_unstemmed | A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges |
| title_short | A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges |
| title_sort | series solution for the vibration of mindlin rectangular plates with elastic point supports around the edges |
| url | http://dx.doi.org/10.1155/2018/8562079 |
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