|Table of Contents|

[1] Huang Bin*,. One Computational Method of the Eigenvaluesof the Horizontal Vibration Problem of Beam [J]. Journal of Southeast University (English Edition), 2002, 18 (3): 277-282. [doi:10.3969/j.issn.1003-7985.2002.03.017]
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One Computational Method of the Eigenvaluesof the Horizontal Vibration Problem of Beam()
梁横向振动问题的特征值的一种算法
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
18
Issue:
2002 3
Page:
277-282
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2002-09-30

Info

Title:
One Computational Method of the Eigenvaluesof the Horizontal Vibration Problem of Beam
梁横向振动问题的特征值的一种算法
Author(s):
Huang Bin*
Department of Engineering, Jinling Institute of Technology, Nanjing 210038, China
黄滨
金陵科技学院工程系, 南京 210038
Keywords:
horizontal vibration problem of beam;  eigenvalue;  eigenfunction;  Galerkin method
梁横向振动问题;  特征值;  特征函数;  Galerkin方法
PACS:
O175.1
DOI:
10.3969/j.issn.1003-7985.2002.03.017
Abstract:
This paper considers one computational method of the eigenvalues’ approximate value of the horizontal vibration problem of beam. The proof of our main result is based on the variational formula. First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the (n-1)-th approximate value is estimated by the n-th approximate value. When n is increased, the accuracy of eigenvalue λk is increased. When n is appropriately selected, the accuracy of λk we need is obtained. This computational method is significant both in applications and in theory.
本文考虑计算梁横向振动问题的特征值的近似值的一种算法. 主要结果的证明运用变分公式. 首先利用Cauchy不等式证明了一个基本不等式;其次采用Galerkin方法来构造适当的基函数, 并利用Cauchy不等式给出了其特征值计算的误差估计式;最后得到计算梁横向振动问题的特征值的近似值的算法, 而且可以用第n次近似值来估计第n-1次的近似值的精确度. 随着n的增大, 特征值λk的精确度逐步提高, 只要适当选取n, 就可以求得所要精确度的特征值的近似值. 这个算法具有广泛的实用价值和理论价值.

References:

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Memo

Memo:
* Born in 1958, male, lecturer.
Last Update: 2002-09-20