Title: Solution of Eigenvalue Problems for Nonclassically Damped Systems
Abstract: A solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of nonclassically damped structural systems. The proposed method is obtained by applying the modified Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem. In the iteration methods, such as the inverse iteration method and the subspace iteration method, singularity may be occurred during the factorizing process when the shift value is close to an eigenvalus of the system. However, even through the shift value is an eigenvalue of the system, the proposed method provides nonsingularity, if the desired eigenvalue is not multiple, and that is analytically proved. Since the modified Newton-Raphson technique is adopted to the proposed method, initial values are need. The initial values of the proposed method can be obtained by the intermediate results of iteration methods or results of approximate methods. Because the Lanczos method effectively produces better initial values than other methods, the results of the Lanczos method are taken as the initial values of the proposed method. Two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well-known subspace iteration method and the Lanczos method.
Publication Year: 1997
Publication Date: 1997-01-01
Language: en
Type: article
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