Volume 6, Issue 3 (September 2008)
IJCE 2008, 6(3): 216-225 |
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Kaveh A, Najimi M. Variation Theorems for Dynamic Analysis of 2D Structures. IJCE 2008; 6 (3) :216-225
URL: http://ijce.iust.ac.ir/article-1-181-en.html
URL: http://ijce.iust.ac.ir/article-1-181-en.html
Abstract: (9915 Views)
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.
Keywords: Structural variation theorems, Inverse vector iteration method, Rayleigh\'s quotient, Eigenvalues, Eigenvectors and Gram-Schmidt Orthogonalization
Type of Study: Technical Note |
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