異向彈性體內線波源之反射及透射波前的建構

Construction of Reflective and Refractive Wave Fronts Due to a Line Source in Anisotropic Elastic Media

黃渝婷(Yu-Ting Huang)

指導教授 ： 吳光鐘

國立臺灣大學/工學院/應用力學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01081

摘要

本文發展一建構反射和透射波前的方法，使之能處理二維異向彈性介質中線波源之波傳問題。理論之基礎為利用廣義Snell’s Law中外觀波速在反射(透射)前後保持不變的定律，去求解反射(透射)後，波的射線速度向量。射線速度的數值解可利用外觀波速和一六維特徵值問題的特徵值及其微分組合表達，其與波曲線圖互有對應關係。本文求解的問題有水平、傾斜、正方形及圓形邊界等情況下之反射和透射波前，主要為一次和二次的反射及透射波前曲線建構。

關鍵字

異向彈性力學 ； 波傳 ； 波前 ； 傾斜層

並列摘要

A method to deal with the two dimensional wave propagation problem, and to construct the reflective and refractive wave fronts of a line source in anisotropic elastic media is developed in this thesis. The basic theory of this method is to use the generalized Snell’s Law which describes that the apparent wave speed always remains unchanged before or after reflection (refraction). Using this law to trace the energy velocity vectors. And the values of them could be solved from a six-dimensional eigenvalue problem and be presented by the combination of eigenvalue p and its differential. The energy velocity vector is relative to the wavefront curve.
The problems being solved in this thesis are horizontal, inclined, rectangular, and circular geometric boundary. Primarily construct the first and the second reflective and refractive wave fronts.

並列關鍵字

anisotropic elasticity ； wave propagation ； wave front ； dipping layer

參考文獻

[3] 洪書昀，(2006)，「含孔洞無限域受平面P波入射之動態反應」，國立臺灣大學土木工程研究所碩士論文。

[2] 陳世豪，(2003)，「動態埋藏源於異向彈性多層介質內之暫態分析」，國立臺灣大學應用力學研究所博士論文。

[5] Achenbach, J. D. (1973). Wave propagation in elastic solids: North-Holland.

[6] Payton, R. G. (1983). Elastic wave propagation in transversely isotropic media: Springer.

[7] Osher, S., Cheng, L.-T., Kang, M., Shim, H., and Tsai, Y.-H. (2002). Geometric optics in a phase-space-based level set and Eulerian framework1. Journal of computational physics, 179(2), 622-648.