A PERTURBATION METHOD FOR REDUCTION OF EIGENVALUE ANALYSIS OF STRUCTURES WITH LARGE STIFFNESSES AND SMALL MASSES

A perturbation method to reduce the computing time for the eigenvalue analysis of structural dynamics is introduced in this paper. A simpliÞed structural model, in which the degrees of freedom associated with the large sti¤nesses are eliminated from the eigenvalue equation and the small masses are not considered, is set up and analysed. The eigenvalues and eigenvectors are served as the zeroth-order solution and a perturbation procedure is performed to restore the eigensolution for the model of full degrees of freedom. The method is successfully applied to the plane frame. The numerical results show that the computing time can be greatly reduced while the high accuracy for the eigensolution is achieved. The good perturbed result of both eigenvalues and eigenvectors is obtained even from the Þrst-order perturbation and the accurate normality of eigenvectors is achieved in the higher-order perturbation. For the perturbation with small masses, a step perturbation is suggested to obtain a better result