Variation Theorems for Dynamic Analysis of 2D Structures

In this paper, the rayleigh's quotient and the inverse vector iteration method are presented. thelatter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vectoriteration method with shifting enables to determine the higher modes. first some basic theorems of linearalgebra are presented and extended to study the free vibration of structures. then the variation theorems arepresented for predicting the eigenvalues and eigenvectors of the modified structures. these theorems reducethe number of cycles of the iterations used for calculating the eigenvalues and eigenvectors of the modifiedstructures. finally. an example is solved to show the ability of the present approach.