| 平行四边形薄板自由振动的康氏法解 |
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| 引用本文： | 梁枢平,陈文. 平行四边形薄板自由振动的康氏法解[J]. 华中科技大学学报(自然科学版), 1990, 0(5) |
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| 作者姓名： | 梁枢平 陈文 |
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| 作者单位： | 华中理工大学力学系(梁枢平)，江苏镇江路面机械总厂(陈文) |
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| 摘 要： | 本文首先采用一个线性变换将平行四边形域上的边值问题变换到矩形域。然后在王磊教授工作的基础上再次采用康托洛维奇能量近似法结合广义梁函数,导得板振动的一个常微分方程及边界条件。采用“对分法”求解了18种边界条件下不同斜度的平行四边形板,得到板的振动频率。本文所采用的方法较原有方法计算工作量大为减少,且具有相当高的精度。
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| 关 键 词： | 弹性力学 康托洛维奇法 广义梁函数 自由振动 平行四边形薄板 |
The Kantorovich Solution for the Free Vibration of a Parallelogram Thin Plate |
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| Liang Shuping Chen Wen. The Kantorovich Solution for the Free Vibration of a Parallelogram Thin Plate[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 1990, 0(5) |
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| Authors: | Liang Shuping Chen Wen |
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| Affiliation: | Liang Shuping Chen Wen |
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| Abstract: | A linear transformation is used to transform the boundary value problem in a parallelogram region into one in a rectangular region. By the Kantorovich approximation method with generalized beam functions, an ordinary differential equation and the boundary conditions for plate vibrations are derived. The vibration frequencies of the plates can be found with eighteen types of boundary conditions and various inclined angles. The method proposed is found to be simpler and more convenient than those in current use. |
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| Keywords: | Theory of elasticity Kantorovich method Generalized beam function Parallelogram thin plate Free vibration |
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