Null-field boundary integral equation approach for scattering problem of canyon or hill containing circular or elliptic boundary subject to SH-wave

• Main Authors: Yu Fan, 范羽
• Other Authors: Jeng-Tzong Chen
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/41429751772225064576

碩士 === 國立臺灣海洋大學 === 河海工程學系 === 100 === Scattering problem of seismic wave is an important issue for studying earthquake in seismology. In this thesis, we employed the null-field boundary integral equation approach in conjunction with degenerate kernels and Fourier series (eigenfunction expansion) to solve the SH-wave scattering problems containing circular (elliptic) boundary. By expanding the fundamental solution to degenerate kernels in the polar coordinates (elliptic coordinates), the collocation points could located on the real boundary of problem, and the boundary densities for circular (elliptic) boundaries were expanded by using Fourier series (eigenfunction expansion) in the polar coordinates (elliptic coordinates). The advantages of null-field boundary integral equation approach were (1) free from calculating the principal value, (2) well-posed system, (3) exponential convergence, (4) no boundary-layer effect and (5) meshless. This approach was also a semi-analytical approach since the error came from the number of truncation terms of the Fourier series (eigenfunction expansion). After imbedding the original problem to an infinite domain, the scattering problem could be decomposed to multi-regions for creating complete circular (elliptic) boundary. Therefore, the null-field boundary integral equation could fully use for the scattering problem, and a linear algebraic system could be constructed. In this thesis, the problems of circular-arc canyon, elliptic-arc canyon, circular-arc hill and elliptic-arc hill were considered. The parameter studies of different incident angles of SH-wave and dimensionless frequency were investigated, and the focusing effect was also observed in the case of hill.