A. Kaveh, M. Najimi,
Volume 6, Issue 3 (9-2008)
Abstract
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.