[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()

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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

Author(s):

Huang Bin^*

Department of Engineering, Jinling Institute of Technology, Nanjing 210038, China

Keywords:

horizontal vibration problem of beam;  eigenvalue;  eigenfunction;  Galerkin method

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 λ_k is increased. When n is appropriately selected, the accuracy of λ_k we need is obtained. This computational method is significant both in applications and in theory.

References:

[1] Hile G N, Protter M H. Inequalities for eigenvalue of the Laplacian[J]. Indiana Univ Math, 1980, 29:523-538.
[2] Hile G N, Yeh R Z. Inequalities for eigenvalue of the biharmonic operator[J]. Pacific J Math, 1984, 112:115-133.
[3] Chen Z C, Qian C L. Esttimates for discrete spectrum of Laplacian operator with any order[J]. China Univ Sci Tech, 1990, 20: 259-265.
[4] Protter M H. Can one hear the shape of a drum?[J]. SIAM Rev, 1987, 29:185-197.
[5] Chen Z C, Qian C L. On the upper bound of eigenvalue for elliptic equations with higher orders[J]. Math Anal Appl, 1994, 186:821-834.
[6] Gu Yu, Qian Chunlin. The computation method of first eigenvalue of differential equation[J]. Chinese Electronic Education, 1996, (7): 7-10.(in Chinese)

Memo

Memo:

* Born in 1958, male, lecturer.

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