Efficient free vibration analysis of large structures with close or multiple natural frequencies. Part I: Undamped structures - Lee, In-Won; Jung, Hyung-Jo; Kim, Man-Cheol (Computer Assisted Methods in Engineering and Science, 2023)
An efficient numerical method which can calculate the eigenproblem for the large structural system with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method to the transformed problem. The method can calculate the natural frequencies and mode shapes without any numerical instability which may be encountered in the well-known methods such as the subspace iteration method or the determinant search method which has been widely used for solving eigenvalue problem. The efficiency of the method is verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.