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Please use this identifier to cite or link to this item: http://ntour.ntou.edu.tw:8080/ir/handle/987654321/24395

Title: Mathematical analysis and numerical study to free vibrations of annular plates using BIEM and BEM
Authors: J. T. Chen;S. Y. Lin;I. L. Chen;Y. T. Lee
Contributors: NTOU:Department of Harbor and River Engineering
Keywords: boundary integral equation method;boundary element method;annular plate;spurious eigenvalue;degenerate kernel;Fourier series;circulants;SVD technique of updating term;Burton and Miller method;CHIEF method
Date: 2006-01-08
Issue Date: 2011-10-20T08:12:06Z
Publisher: International Journal for Numerical Methods in Engineering
Abstract: abstract:In this paper, the spurious eigenequations for annular plate eigenproblems by using BIEM and BEM are studied in the continuous and discrete systems. Since any two boundary integral equations in the plate formulation (4 equations) can be chosen, 6 (C) options can be considered instead of only two approaches (single-layer and double-layer methods, or singular and hypersingular equations) which are adopted for the eigenproblems of the membrane and acoustic problems. The occurring mechanism of the spurious eigenequation for annular plates in the complex-valued formulations is studied analytically. For the continuous system, degenerate kernels for the fundamental solution and the Fourier series expansion for the circular boundary density are employed to derive the true and spurious eigenequations analytically. For the discrete system, the degenerate kernels for the fundamental solution and circulants resulting from the circular boundary are employed to determine the true and spurious eigenequations. True eigenequation depends on the specified boundary condition while spurious eigenequation is embedded in each formulation. It is found that the spurious eigenvalue for the annular plate is the true eigenvalue of the associated interior problem with an inner radius of the annular domain. Also, we provide three methods (SVD updating technique, Burton and Miller method and CHIEF method) to suppress the occurrence of the spurious eigenvalues. Several examples were demonstrated to check the validity of the formulations.
Relation: 65(2), pp.236–263
URI: http://ntour.ntou.edu.tw/handle/987654321/24395
Appears in Collections:[河海工程學系] 期刊論文

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