Abstract
An efficient numerical method which can analyze the eigenproblem for the large structural system with multiple or close eigenvalues is presented. This method is formulated by applying the accelerated Newton-Raphson method to obtained from the solution of a constrained stationary value problem. The step length used in the accelerated Newton-Raphson method is calculated by the least square concept. This method can calculate the natural frequencies and mode shapes without any numerical instability which may be often 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 this method is verified by comparing convergence and solution time for numerical examples with those of the subspace iteration method and the determinant search method.
Similar content being viewed by others
References
Bathe, K. J., 1982,Finite Element Procedures in Engineering Analysis, Prentice-Hall.
Bathe, K. J. and Ramaswamy, S., 1980, “An Accelerated Subspace Iteration Method,”Computer Methods in Appl. Mech. and Eng., Vol. 23, pp. 313–331.
Bathe, K. J. and Wilson, E. L., 1973, “Eigensolution of Large Structural Systems with Small Bandwidth,”J. Eng. Mech. Div., Vol. 99, pp. 467–479.
Habibulah, A. and Wilson, E. L., 1989,SAP90TM Sample Example and Verification Manual, Computers and Structures, Inc.
Lee, I. W., Jung, H. J. and Kim, M. C., 1994, “An Efficient Free Vibration Analysis of Structures with Multiple Natural Frequencies,”Proceedings of the Korea Society of Civil Engineers, pp. 135–138.
Lee, I. W. and Robinson, A. R., 1979, “Solution techniques for Large Eigenvalue Problems in Structural Dynamics,”Structural Research Series No. 462, University of Illinois.
Wilson, E. L. and Itoh, T., 1983, “An Eigensolution strategy for Large Systems,”Comp. Struct., Vol. 16, pp. 259–265.
1983,ADINA System Verification Manual, ADINA Engineering, Inc.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lee, I.W., Jung, H.J., Kim, M.C. et al. Modified inverse iteration method using the side condition and the step length. KSME Journal 10, 64–71 (1996). https://doi.org/10.1007/BF02953945
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02953945