COMPUTER ASSISTED PROOF OF SPURIOUS EIGENSOLUTION FOR ANNULAR AND ECCENTRIC MEMBRANES

Authors

I-Lin Chen, Department of Naval Architecture, National Kaohsiung Marine University, Kaohsiung, Taiwan.
Jeng-Tzong Chen, Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan. Department of Mechanical and Mechanical Engineering, National Taiwan Ocean University, Keelung, Taiwan.Follow
Wei-Ming Lee, Department of Mechanical Engineering, China Institute of Technology, Taipei, Taiwan.
Shang-Kai Kao, Department of Harbor and River Engineering, National Taiwan Ocean University, Keelung, Taiwan.

Abstract

Spurious eigensolutions in the boundary integral equation (BIE) or boundary element method (BEM) for doublyconnected domain problems, the eccentric and annular membranes, are studied analytically and numerically in this paper. For the mathematical analysis, we employ the null-field integral equation, the degenerate kernels and the Fourier series to prove the existence of spurious eigensolutions in the continuous system. Examples of eccentric case, annular membrane and general shape are solved by using the null-field equation approach and BEM, respectively. Based on the numerical experiment, computer-assisted proof for the existence of spurious eigenvalues in companion with the trivial outer boundary data is given. The spurious eigenvalue is found to be the true eigenvalue of a circular membrane with the inner radius. The SVD structure for the four influence matrices is examined. Also, the trivial outer boundary densities are found in case of spurious eigenvalues and are shown in the bar chart.

Recommended Citation

Chen, I-Lin; Chen, Jeng-Tzong; Lee, Wei-Ming; and Kao, Shang-Kai (2009) "COMPUTER ASSISTED PROOF OF SPURIOUS EIGENSOLUTION FOR ANNULAR AND ECCENTRIC MEMBRANES," Journal of Marine Science and Technology: Vol. 17: Iss. 3, Article 6.
DOI: 10.51400/2709-6998.1957
Available at: https://jmstt.ntou.edu.tw/journal/vol17/iss3/6