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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24341

Title: Applications of dual MRM for determining the natural frequencies and natural modes of an Euler–Bernoulli beam using the singular value decomposition method
Authors: W. Yeih;J.T. Chen;C.M. Chang
Contributors: NTOU:Department of Harbor and River Engineering
Keywords: Dual multiple reciprocity method;Beam;Natural modes;Singular value decomposition
Date: 1999-04
Issue Date: 2011-10-20T08:11:32Z
Publisher: Engineering Analysis with Boundary Elements
Abstract: abstract:In this paper, a dual multiple reciprocity method (MRM) is employed to solve the natural frequencies and natural modes for an Euler–Bernoulli beam. It is found that the conventional MRM using an essential integral equation results in spurious eigenvalues and modes. By using the natural integral equation of dual MRM, the spurious eigendata can be filtered out. Four numerical examples are given to verify the validity of the present formulation. In one of these four examples, fixed–fixed supported beam, it is found that the boundary eigenvector cannot be determined by either the essential or natural integral equation alone since the rank of the corresponding leading coefficient matrix is insufficient. The singular value decomposition method is then used to solve the eigenproblem after combining the essential and natural integral equations. This method can avoid the spurious eigenvalue problem and possible indeterminancy of boundary eigenvectors at the same time.
Relation: 23(4), pp.339–360
URI: http://ntour.ntou.edu.tw/handle/987654321/24341
Appears in Collections:[河海工程學系] 期刊論文

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