臺灣博碩士論文加值系統

　　本文利用積分轉換的技巧並透過矩陣Bromwich展開法及Cagniard逆積分轉換法，成功地解析三維層狀介質中的暫態彈性波傳問題，並以一薄層覆於半無窮域固體受表面一點集中力為數值計算例，配合音射實驗來檢證理論與計算的正確性。
　　本文首先處理邊界值問題，所有的載荷均位於界面或邊界上，再將所獲得的矩陣解推廣至域內受各種不同加載的情況。本文簡潔地以矩陣形式之無窮級數表現此三維層狀介質受動力載荷的問題在積分轉換域中的波動射線解；級數中的第每一項，分別代表經界面反射或透射不同次數的波之總和，其具明顯之物理意義。在數值計算方面，本文利用矩陣解的特性提出一確實可行的方法，可處理波的退化的問題，而使得較長時間的暫態波傳計算變成可行。
　　本文亦由三維系統的建構中直接獲得二維平面問題的解析；提出二維問題與三維問題在轉換域中的對應關係，使得此兩類問題可同時獲得解決。

　　In this thesis, the transient waves propagating in three dimensional layered medium subjected to arbitrarily oriented loadings are solved with aids of the integral transform technique and the Cagniard method for the inverting transformation. The numerical calcuations are conducted on a thin layer overlying a solid half space and the free surface is subjected to a concentrated dynamic force. The numerical calculations are compared with experimental measurements to verify the accuracy of theoretical model and numerical calculation.
　　In this study, loadings applied at the interfaces and boundaries of the layered medium are treated first and then extended to those applied at the interior. The ray solution for the layered medium is expressed concisely in terms of an infinite power matrix series. The solution is then decomposed into infinite wave groups in which the waves are reflected by ofr transmitted through the interface the same times. Each multi-reflected wave can be verified by the theory of generalized ray. For the numeical calculation, a method which can be used to obtain the longer time resposes for the layered medium subjected to a dynamic loading are pressented.
　　The transient two dimnensional solutions for waves propagating in layered medium are also obtained in this thesis directly through the construction of solutions for three dimensional cases. The correspondence relationships in the transformed domain between two and three dimensional problems are presented so that these two kinds of problems can be solved at one time.