Study on true and spurious eigenvalues of elliptical membranes and plates by using imaginary part of the fundamental solutions

• Main Authors: Wen-Che Lee, 李文哲
• Other Authors: Jeng-Tzong Chen
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/48004424858638547307

碩士 === 國立臺灣海洋大學 === 河海工程學系 === 99 === In this thesis, we employ the imaginary-part of the fundamental solutions to determine the true and spurious eigenvalues of an elliptical membrane and plate. We focus on the non-dimensional dynamic influence function (NDIF) method by utilizing the imaginary-part of the fundamental solution. The NDIF method belongs to one kind of meshless methods. The coefficients of influence matrices in the NDIF method can be easily determined according to the distance between source and collocation points. In order to demonstrate the validity of numerical results, we employ the imaginary-part indirect boundary integral equation method (BIEM) to examine why spurious eigenvalues occur. This imaginary-part indirect BIEM is one kind of semi-analytical methods. The approach is utilized in conjunction with the degenerate kernel and the eigenfunction expansion for the closed-form fundamental solution and unknown coefficients, respectively. To fully employ the elliptical geometry for an analytical study, the elliptic coordinate system in companion with the Mathieu functions is used. Owing to the appearance of spurious eigensolutions accompanied with true eigensolutions, singular value decomposition (SVD) updating techniques are employed to extract true and spurious eigenvalues out. Finally, the occurring mechanism of true and spurious eigenvalues for the elliptical membrane and plate are analytically investigated and numerically implemented. Also, the numerical results are used to verify the validity of the proposed approach.