Accurate and fast three-dimensional free vibration analysis of large complex structures using the finite element method

Abstract

Free vibration analysis of large complex structures with improved Lanczos iteration method is investigated through the finite element method. An important step in the traditional Lanczos iteration method for large generalized eigenvalue problems arising from free vibration analysis is that large-scale sparse linear system must be repeatedly solved within each step of the Lanczos iteration, which generally accounts for 70% to 90% of the calculation time of the eigenvalue problems. In the improved Lanczos iteration method given here, three-level preconditioner is proposed and utilized to improve the computational performance of Lanczos iteration. In this way, the multifrontal block incomplete Cholesky (MFBIC) preconditioner and p-type multigrid preconditioner based on higher-order hierarchical basis functions are proposed and utilized to improve the computational performance and decrease the memory requirements. To further reduce the memory consumption, the block Jacobi preconditioner is introduced in the Lanczos iteration, and a new three-level preconditioner that combines MFBIC, p-type multigrid and block Jacobi is proposed. The accuracy and performance of the improved method has been compared with exact solution, basic method and ANSYS. It is shown that this free vibration analysis method can be extremely useful to design structure dynamic characteristics of large complex structures.