چكيده لاتين :
In this paper, the Rayleighיs 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. First some basic theorems of linear
algebra are presented and extended to study the free vibration of structures. Then 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.
