A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method
The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unif...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/7470460 |
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| _version_ | 1832564847260205056 |
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| author | Yuan Du Liping Sun Xuhong Miao Fuzhen Pang Haichao Li Siyu Wang |
| author_facet | Yuan Du Liping Sun Xuhong Miao Fuzhen Pang Haichao Li Siyu Wang |
| author_sort | Yuan Du |
| collection | DOAJ |
| description | The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported. |
| format | Article |
| id | doaj-art-b1f36eb366914a4f929d33da90bb0421 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-b1f36eb366914a4f929d33da90bb04212025-02-03T01:10:02ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/74704607470460A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz MethodYuan Du0Liping Sun1Xuhong Miao2Fuzhen Pang3Haichao Li4Siyu Wang5College 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, ChinaThe free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.http://dx.doi.org/10.1155/2019/7470460 |
| spellingShingle | Yuan Du Liping Sun Xuhong Miao Fuzhen Pang Haichao Li Siyu Wang A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method Shock and Vibration |
| title | A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method |
| title_full | A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method |
| title_fullStr | A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method |
| title_full_unstemmed | A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method |
| title_short | A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method |
| title_sort | unified formulation for free vibration of spherical cap based on the ritz method |
| url | http://dx.doi.org/10.1155/2019/7470460 |
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