A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates
The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coef...
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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/10.1155/2018/1071830 |
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| author | Supun Jayasinghe Seyed M. Hashemi |
| author_facet | Supun Jayasinghe Seyed M. Hashemi |
| author_sort | Supun Jayasinghe |
| collection | DOAJ |
| description | The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB®, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS® and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins. |
| format | Article |
| id | doaj-art-1be7b976008c42508ba27f54e7e35bfc |
| 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-1be7b976008c42508ba27f54e7e35bfc2025-08-20T03:54:51ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/10718301071830A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic PlatesSupun Jayasinghe0Seyed M. Hashemi1Department of Aerospace Engineering, Ryerson University, Toronto, CanadaDepartment of Aerospace Engineering, Ryerson University, Toronto, CanadaThe free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB®, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS® and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.http://dx.doi.org/10.1155/2018/1071830 |
| spellingShingle | Supun Jayasinghe Seyed M. Hashemi A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates Shock and Vibration |
| title | A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates |
| title_full | A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates |
| title_fullStr | A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates |
| title_full_unstemmed | A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates |
| title_short | A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates |
| title_sort | dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates |
| url | http://dx.doi.org/10.1155/2018/1071830 |
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