Spurious eigenvalues and fictitious frequencies for acoustic problems with the mixed-type boundary conditions by using BEM

• Main Authors: Lin Tzong-Wey, 林宗衛
• Other Authors: Chen Jeng-Tzong
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/82619128095906223371

碩士 === 國立海洋大學 === 河海工程學系 === 91 === In this thesis, boundary integral equations and boundary element methods were employed semi-analytically and numerically to study on the occurrence of both the spurious eigenvalues and fictitious frequencies for the interior and exterior Helmholtz equations with the mixed-type boundary conditions, respectively. For the interior acoustic problem, the degenerate kernels of fundamental function and Fourier series were utilized for null-field equation to derive the true and spurious eigenfunctions analytically. The complex-valued BEM, the real-part BEM, the imaginary-part BEM and the MRM were utilized to solve the eigenproblem and eigenmodes. The results are compared with FEM. Moreover, the SVD updating techniques in conjunction with the Fredholm''s alternative theorem were adapted to sort out the spurious eigenvalues and extract out the true ones. For the exterior radiation problem, the same mathematical tools were utilized to derive the field solution analytically. The complex-valued BEM was utilized to solve the fictitious frequencies in the exterior acoustic problem. The CHIEF and Burton \& Miller methods were adopted to suppress the occurrence of the fictitious frequencies. It is emphasized that the occurrence of not only spurious eigenvalues but also fictitious frequencies depend on the adopted method (singular or hypersingular formulation) no matter what the given types of boundary conditions for the problem are. The illustrative examples were verified successfully.