本研究主要目的了解彎管對導波波傳之影響，彎管是現場管路系統中常見的的特徵之一，在實際檢測上，當訊號傳遞通過彎管時會有波式轉換現象的發生，造成訊號的非對稱性提高，增加檢測的困難度。
本研究的內容包括應用有限元素之振動分析求解4種不同彎曲半徑之彎管頻散曲線，4種彎曲半徑分別為：1.0 m、0.6 m、0.4 m、0.2 m，並且利用波傳模擬與實驗檢測來驗證彎管頻散曲線的正確性。研究發現，彎管有著與直管相似的頻散曲線，其中彎管中T(0,1)模態與直管T(0,1)模態頻散最為相似，研究也發現，當彎曲半徑越大，彎管的頻散曲線會越接近直管。雖然彎管與直管有著相似的頻散曲線，但是因為彎管幾何形狀之因素，會造成彎管同一圓周截面上的各節點所接收波傳訊號會有時間延遲(Time Delay)以及波形失真（Distortion）之效應，因而發生波式轉換之現象。另由本研究的實驗中得知，雖然位於彎管後方之特徵其訊號因為波式轉換的原因使得回波訊號的非對稱性提高，但是並不會造成回波訊號位置與實際位置之間有所差異。
對於特殊形狀之管線，在實際檢測上會有著較高的複雜性，如能應用振動分析求解該管線之頻散曲線，對於檢測上有著實質的幫助。

In this study, the most part is acquainted with the effect of elbow pipe to the guided wave. Elbow pipes were most seen feature in work environment. It was difficult for inspection that the anti-symmetric of signal increased when it passed the elbow pipe by happening mode conversion. The study content includes the using modal solution of the finite element method to solve the dispersion curve of four different bend radius of elbow pipe, they were : 1.0 m, 0.6 m, 0.4 m and 0.2 m. Therefore, by using simulation of wave propagation and experiment to verify dispersion curve of bend pipe were accuracy. This study reveals that, the dispersion curve of elbow pipe is similar to that of straight pipe, and T(0,1) mode in the elbow pipe is most similar with it in straight pipe. Thus, the dispersion curve in elbow pipe and straight pipe were similar, but the effect of geometry of elbow pipe will make the symmetrical incident signal time delay and wave front will distortion, and then it will cause mode conversion.
According to the experiment of this study, although the signal of feature behind the elbow pipe caused by mode conversion will make anti-symmetry of reflection signal increase, it still won’t make shift between reflection signal location and real feature location. It is very difficult and complex for inspecting the particular geometry pipe. If we can use the modal analysis of finite element method to solve the dispersion curve of particular geometry pipe, the inspection can be improve.

中文摘要 i
英文摘要 ii
目錄 iii
表目錄 vi
圖目錄 vii
第一章 緒論 1
1.1前言 1
1.2文獻回顧 3
1.3研究方法 8
第二章 基本理論 12
2.1導波在圓管中傳播的波動方程式 12
2.1.1縱向模態 15
2.1.2扭矩模態 15
2.1.3撓曲模態 16
2.2頻散曲線 17
2.3波形結構 19
2.4波式轉換 20

第三章 模擬設定 28
3.1 ANSYS有限元素軟體 28
3.2有限元素振動分析模型之設定 29
3.2.1振動分析之直管有線元素模型設定 29
3.2.2振動分析之彎管有線元素模型設定 33
3.2.3暫態分析之導波波傳模擬設定 34
第四章 實驗架設 43
4.1 實驗設備儀器 43
4.2實驗步驟 47
第五章 結果與討論 55
5.1應用有限元素分法振動分析求解頻散曲線之結果 55
5.1.1直管頻散曲線之結果與討論 55
5.1.2彎管頻散曲線之結果與討論 56
5.2導波波傳模擬之結果與分析 58
5.3實驗結果與分析 61
5.4彎管波式轉換之討論 62
第六章 結論與未來展望 80
6.1結論 80
6.2未來展望 83
參考文獻 84

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