American Society of Civil Engineers


Eigensolution Method for Structures with Multiple or Close Eigenvalues


by In-Won Lee, (Prof., Dept. of Civ. Engrg., Korea Advanced Inst. of Sci. and Tech., Taejon 305-701, South Korea), Hyung-Jo Jung, (Grad. Student, Dept. of Civ. Engrg., Korea Advanced Inst. of Sci. and Tech., Taejon 305-701, South Korea), Man-Cheol Kim, (Grad. Student, Dept. of Civ. Engrg., Korea Advanced Inst. of Sci. and Tech., Taejon 305-701, South Korea), and Arthur R. Robinson, (Prof. Emeritus, Dept. of Civ. Engrg., Univ. of Illinois at Urbana-Champaign, Urbana, IL 61801)

Journal of Engineering Mechanics, Vol. 125, No. 11, November 1999, pp. 1286-1292, (doi:  http://dx.doi.org/10.1061/(ASCE)0733-9399(1999)125:11(1286))

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Document type: Journal Paper
Abstract: A solution method that can calculate the eigenproblem for large structures with multiple or close natural frequencies is presented. The method is formulated by the accelerated Newton-Raphson method for the transformed problem. The method can calculate the natural frequencies and mode shapes without any of the numerical instability that may be encountered in the inverse iteration process with a shift of the well-known methods, such as the subspace iteration method or the determinant search method, which have been widely used for solving an eigenproblem. The efficiency of the method is verified by comparing convergence and solution times for numerical examples with those of the subspace iteration method and the determinant search method.


ASCE Subject Headings:
Eigenvalues
Natural frequency
Numerical analysis
Stability
Structures