| 层合圆板轴对称自由振动问题的精确解 |
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| 引用本文： | 范家让,叶建乔. 层合圆板轴对称自由振动问题的精确解[J]. 合肥工业大学学报(自然科学版), 1990, 0(2) |
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| 作者姓名： | 范家让 叶建乔 |
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| 摘 要： | 本文从三维弹性力学基本方程出发,抛弃任何有关位移模式和应力分布的假设,建立了横观各向同性层合圆板轴对称自由振动问题的状态方程。给出了本问题的精确解式。此解满足弹性力学全部方程,并计及了所有独立的弹性常数。无论层数多少,最后都归结为解二元一次联立代数方程。数值结果和Reissner理论、Mindlin理论以及有关文献作了对比,结果令人满意。
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| 关 键 词： | 横观各向同性体 层合圆板 自由振动 状态方程 Cayley-Hamilton定理 |
EXACT SOLUTIONS FOR AXISYMMETRIC FREE VIBRATION OF LAMINATED CIRCULAR PLATES |
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| Fan Jiarang Ye Jianqiao. EXACT SOLUTIONS FOR AXISYMMETRIC FREE VIBRATION OF LAMINATED CIRCULAR PLATES[J]. Journal of Hefei University of Technology(Natural Science), 1990, 0(2) |
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| Authors: | Fan Jiarang Ye Jianqiao |
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| Affiliation: | Fan Jiarang Ye Jianqiao |
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| Abstract: | Basing on the fundamental equations of three dimensional elasticity and giving up any assumptions about displacement models and stress distributions the state equations for axisymmetric free vibration of laminated transversely isotropic circular plates arc established and the exact sclutions for such problems are presented in this paper. Every fundamental equation of three dimensional elaticity can be exactly satisfied and all the elastic constants can also be taken into account by present method. No matter how many layers arc considered'the calculation always leads to solving a set of linear algebraic equations of 2nd order. Numerical results arc obtained and compared with those of Reissner's, Mindiin's theories and some references. |
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| Keywords: | Transversely isotropic body Laminated circular plate Free vibration State eguation Cayley-Hamilton theorem. |
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