In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions
In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/653836 |
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| author | Xianjie Shi Dongyan Shi Zhengrong Qin Qingshan Wang |
| author_facet | Xianjie Shi Dongyan Shi Zhengrong Qin Qingshan Wang |
| author_sort | Xianjie Shi |
| collection | DOAJ |
| description | In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions. |
| format | Article |
| id | doaj-art-e240969280a1473b95f7f2a2edba4834 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-e240969280a1473b95f7f2a2edba48342025-08-20T02:21:13ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/653836653836In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary ConditionsXianjie Shi0Dongyan Shi1Zhengrong Qin2Qingshan Wang3College 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, ChinaIn comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.http://dx.doi.org/10.1155/2014/653836 |
| spellingShingle | Xianjie Shi Dongyan Shi Zhengrong Qin Qingshan Wang In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions The Scientific World Journal |
| title | In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions |
| title_full | In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions |
| title_fullStr | In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions |
| title_full_unstemmed | In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions |
| title_short | In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions |
| title_sort | in plane vibration analysis of annular plates with arbitrary boundary conditions |
| url | http://dx.doi.org/10.1155/2014/653836 |
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