Efficient free vibration analysis of large structures with close or multiple natural frequencies. Part I: Undamped structures

  • In-Won Lee Korea Advanced Institute of Science and Technology
  • Hyung-Jo Jung Korea Advanced Institute of Science and Technology
  • Man-Cheol Kim Korea Advanced Institute of Science and Technology

Abstract

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.

Keywords

free vibration analysis, accelerated Newton-Raphson method, multiple or close natural frequencies,

References

[1] ADINA System Verification Manual. ADINA Engineering, Inc., 1983.
[2] K.J. Bathe. Finite Element Procedures in Engineering Analysis. Prentice-Hall, 1982.
[3] K.J. Bathe, E.L. Wilson. Solution methods for eigenvalue problems in structural mechanics. Int. J. Num. Meth. Engrg. 6: 213-226, 1973.
[4] K.J. Bathe, E.L. Wilson. Eigensolution of large structural systems with small bandwidth. J. Eng. Mech. Div. 99: 467- 479, 1973.
[5] K.J. Bathe, S. Ramaswamy. An accelerated subspace iteration method. Computer Methods in Appl. Mech. And Eng. 23: 313- 331, 1980.
Published
May 22, 2023
How to Cite
LEE, In-Won; JUNG, Hyung-Jo; KIM, Man-Cheol. Efficient free vibration analysis of large structures with close or multiple natural frequencies. Part I: Undamped structures. Computer Assisted Methods in Engineering and Science, [S.l.], v. 6, n. 3-4, p. 403-414, may 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1299>. Date accessed: 21 nov. 2024.
Section
Articles