A study on true and spurious eigensolutions of two-dimensional acoustic cavities

• Main Authors: Chuan Xia Huang, 黃川夏
• Other Authors: Jeng Tzong Chen
• Format: Others
• Language: en_US
• Published: 1999
• Online Access: http://ndltd.ncl.edu.tw/handle/17837086705309036014

碩士 === 國立海洋大學 === 河海工程學系 === 87 === In this thesis, the relation among the dual MRM, the real-part dual BEM and the dual complex-valued BEM was constructed. The former two methods result in spurious eigensolutions for interior problems. Not only analytical study but also numerical experiments were performed to filter out the spurious solutions. For the analytical approach, we employed the theory of circulants to study the mechanism why spurious eigensolutions occur. For the numerical experiments, we developed the DUALMRM and DUALREAL programs to determine the true and spurious solutions. Based on the dual framework, the true and spurious eigenvalues can be separated by combining the singular and hypersingular equations together in conjunction with the singular value decomposition (SVD) technique. The true and spurious eigensolutions (including eigenvalues and eigenfunctions) were investigated analytically and found numerically. Also, the boundary modes and the multiplicity of the true eigenvalues can be determined by using the SVD technique. These two roles of the SVD technique in the dual MRM and the real-part dual BEM were both examined.