Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method
In this investigation, free vibration of stepped circular Mindlin plate with arbitrary boundary conditions is presented by an improved Fourier–Ritz method. Based on the locations of the step variations, the stepped circular plate can be divided into different concentric annular and circular plates....
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2022/1643050 |
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| _version_ | 1832558334482317312 |
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| author | Qingjun Hao Zhaobo Chen Wenjie Zhai |
| author_facet | Qingjun Hao Zhaobo Chen Wenjie Zhai |
| author_sort | Qingjun Hao |
| collection | DOAJ |
| description | In this investigation, free vibration of stepped circular Mindlin plate with arbitrary boundary conditions is presented by an improved Fourier–Ritz method. Based on the locations of the step variations, the stepped circular plate can be divided into different concentric annular and circular plates. The first-order shear deformation plate theory is employed to establish the theoretical model. Once all the displacements of a stepped circular plate are expanded by an improved Fourier series expansion, an exact solution can be obtained based on the Rayleigh–Ritz procedure by the energy function of the current model. The convergence and accuracy of the proposed method are proved by several numerical examples. The effects of classical boundary conditions and geometrical parameters on the frequency parameters of a stepped circular plate are also analyzed. |
| format | Article |
| id | doaj-art-a5d8f83b6e064159aef37ba71c86b480 |
| institution | Kabale University |
| issn | 1875-9203 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-a5d8f83b6e064159aef37ba71c86b4802025-02-03T01:32:37ZengWileyShock and Vibration1875-92032022-01-01202210.1155/2022/1643050Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz MethodQingjun Hao0Zhaobo Chen1Wenjie Zhai2School of Mechatronics EngineeringSchool of Mechatronics EngineeringSchool of Mechatronics EngineeringIn this investigation, free vibration of stepped circular Mindlin plate with arbitrary boundary conditions is presented by an improved Fourier–Ritz method. Based on the locations of the step variations, the stepped circular plate can be divided into different concentric annular and circular plates. The first-order shear deformation plate theory is employed to establish the theoretical model. Once all the displacements of a stepped circular plate are expanded by an improved Fourier series expansion, an exact solution can be obtained based on the Rayleigh–Ritz procedure by the energy function of the current model. The convergence and accuracy of the proposed method are proved by several numerical examples. The effects of classical boundary conditions and geometrical parameters on the frequency parameters of a stepped circular plate are also analyzed.http://dx.doi.org/10.1155/2022/1643050 |
| spellingShingle | Qingjun Hao Zhaobo Chen Wenjie Zhai Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method Shock and Vibration |
| title | Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method |
| title_full | Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method |
| title_fullStr | Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method |
| title_full_unstemmed | Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method |
| title_short | Free Transverse Vibration of Circular Plate of Stepped Thickness with General Boundary Conditions by an Improved Fourier–Ritz Method |
| title_sort | free transverse vibration of circular plate of stepped thickness with general boundary conditions by an improved fourier ritz method |
| url | http://dx.doi.org/10.1155/2022/1643050 |
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