| ANALYTICAL RELATIONS BETWEEN EIGENVALUES OF CIRCULAR PLATE BASED ON VARIOUS PLATE THEORIES |
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| 引用本文： | 马连生,王铁军. ANALYTICAL RELATIONS BETWEEN EIGENVALUES OF CIRCULAR PLATE BASED ON VARIOUS PLATE THEORIES[J]. 应用数学和力学(英文版), 2006, 27(3): 279-286. DOI: 10.1007/s 10483-006-0301-1 |
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| 作者姓名： | 马连生 王铁军 |
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| 作者单位： | Department of Engineering Mechanics MOE Key Laboratory for Strength and Vibration Xi'an Jiaotong University，Xi'an 710049，P. R. China，Department of Engineering Mechanics MOE Key Laboratory for Strength and Vibration，Xi'an Jiaotong University，Xi'an 710049，P. R. China |
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| 基金项目： | Project supported by the National Natural Science Foundation of China （No.10125212） |
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| 摘 要： | Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT), the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory (RPT), analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.
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| 关 键 词： | 解析关系 特征值 圆形板 经典平板理论 减切形变 自然频率 |
| 收稿时间： | 2005-02-16 |
| 修稿时间： | 2005-11-15 |
Analytical relations between eigenvalues of circular plate based on various plate theories |
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| Lian-sheng Ma,Tie-jun Wang. Analytical relations between eigenvalues of circular plate based on various plate theories[J]. Applied Mathematics and Mechanics(English Edition), 2006, 27(3): 279-286. DOI: 10.1007/s 10483-006-0301-1 |
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| Authors: | Lian-sheng Ma Tie-jun Wang |
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| Affiliation: | Department of Engineering Mechanics, MOE Key Laboratory for Strength and Vibration,Xi'an Jiaotong University, Xi'an 710049, P. R. China |
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| Abstract: | Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory(CPT), the first-order shear deformation plate theory(FPT) and the Reddy's third-order shear deformation plate theory (RPT), analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates. |
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| Keywords: | classical plate theory shear deformation plate theory eigenvalue buckling natural frequency |
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