| 弹性地基上四边自由矩形薄板振动分析的Kantorovich法 |
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| 引用本文： | 钟阳,周福霖,张永山.弹性地基上四边自由矩形薄板振动分析的Kantorovich法[J].振动与冲击,2007,26(3):33-36. |
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| 作者姓名： | 钟阳 周福霖 张永山 |
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| 作者单位： | 1. 大连理工大学土木学院,大连,116024
2. 广州大学土木学院,广州,510405 |
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| 摘 要： | 利用延展的Kantorovich法推导出弹性地基上四边自由矩形薄板振动问题的解析解表达式。由于薄板振动的固有频率和振型都用初等函数表达出来，所以，在计算中不需要人为地选取挠度函数，并且只要进行初等函数的迭代计算，同时计算精度是可以控制的。最后还给出了计算实例来验证本文所采用的方法以及所推导的公式的正确性。
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| 关 键 词： | 弹性地基 四边自由矩形薄板 固有频率和振型 Kantorovich法 |
| 修稿时间： | 01 8 2006 12:00AM |
VIBRATION ANALYSIS OF A THIN PLATE ON WINKLER FOUNDATION WITH COMPLETELY FREE BOUNDARY BY KANTOROVICH METHOD |
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| Zhong Yang,Zhou Fu-lin,Zhang Yong-shan.VIBRATION ANALYSIS OF A THIN PLATE ON WINKLER FOUNDATION WITH COMPLETELY FREE BOUNDARY BY KANTOROVICH METHOD[J].Journal of Vibration and Shock,2007,26(3):33-36. |
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| Authors: | Zhong Yang Zhou Fu-lin Zhang Yong-shan |
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| Abstract: | The theoretic solution of natural frequencies and modal shapes of a rectangular thin plate on winkler foundation with completely free boundary is derived by Kantorovich method. Since the natural frequencies and the modal shapes of the rectangular thin plate are expressed in the form of elementary functions, it is easy and fast to conduct the iteration calculation. Meanwhile the computing accuracy can be controlled. In order to prove the correctness of formulation, a numerical example is presented, its results are compared with those of the other reference. |
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| Keywords: | winkler foundation rectangular thin plate with completely free boundary natural frequencies and modal shapes Kantorovich method |
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