International Journal of Civil Engineering
IJCE
Engineering & Technology
http://ijce.iust.ac.ir
18
agent2
1735-0522
2383-3874
10.22068/IJCE
en
jalali
1387
6
1
gregorian
2008
9
1
6
3
online
1
fulltext
en
Variation Theorems for Dynamic Analysis of 2D Structures
Technical Note
Technical Note
In this paper, the Rayleigh's quotient and the inverse vector iteration method are presented. The
latter approach helps to obtain the natural frequencies and mode shapes of a structure. Inverse vector
iteration method with shifting enables to determine the higher modes. Some basic theorems of linear algebra
are presented and extended to study the free vibration of structures. The variation theorems are presented for
predicting the eigenvalues and eigenvectors of the modified structures. These theorems reduce the number of
cycles of the iterations used for calculating the eigenvalues and eigenvectors of the modified structures.
Finally, an example is solved to show the ability of the present approach.
Structural variation theorems, Inverse vector iteration method, Rayleigh\'s quotient, Eigenvalues, Eigenvectors and Gram-Schmidt Orthogonalization
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225
http://ijce.iust.ac.ir/browse.php?a_code=A-10-218-60&slc_lang=en&sid=1
A.
Kaveh
`180031947532846002837`

180031947532846002837
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M.
Najimi
alikaveh@iust.ac.ir
`180031947532846002838`

180031947532846002838
Yes