臺灣博碩士論文加值系統

時間反轉法理論(Time Reversal Method, TRM)現已廣泛應用於水下探測、醫學檢測上以及結構非破壞檢測。理論發展隨著疊代式時間反轉法(Iterative time reversal process)與時間反轉因子分解 (Decomposition of time reversal operator, D.O.R.T.)的出現，解決了許多不利於單純使用時間反轉處理的因素，進一步的拓展了時間反轉理論的應用範圍；而此運用時間反轉因子分解的方式，可去除繁複的疊代實驗流程，直接由數學推導得到疊代後之結果。本研究將應用時間反轉因子理論探討計算平板裂縫之散射係數，以及不同方向之訊號入射裂縫對於散射之影響。
於模擬方面，本研究運用ANSYS有限元素軟體進行模擬平板結構與訊號發射擷取；於訊號分析方面，撰寫MATLAB程式處理應用以及輸出散射幅射圖。首先是分別在一有裂縫與一無裂縫的平板環境下，藉由陣列元件發射與擷取訊號，接著將兩組接收訊號做相減之動作，以取得由裂縫干擾產生之散射訊號。時域下對訊號做摺積等同於在頻域下訊號相乘，由於在頻域下處理相對方便簡易，故將時域下的散射訊號經由快速傅立葉轉換(Fast Fourier Transform, FFT)轉移至頻域處理，將頻域訊號依時間反轉因子理論依序排列成轉移矩陣的模式，再由轉移矩陣計算出散射係數。
透過半圓形及圓形陣列元件將各個角度之散射係數計算出來，畫出散射幅射圖(scattering pattern)，再藉由不同裂縫之形狀和尺寸建立其特性表格，探討不同裂縫之散射特性。藉由此方法建立一套計算裂縫各方向之散射係數流程，期望未來應用於實務上之裂縫偵測，對於非破壞檢測能有進一步的貢獻。

Time Reversal Method (TRM) is now widely used in under water exploration, medical testing and on the structure of non-destructive testing. In theory Iterative Time Reversal Process and Decomposition of Time Reversal Operator (D.O.R.T.) appears to solve many issues, simply are not resolved by utilizing the time reversal method. Further expand the time reversal theory application scope. While using this process for time reversal, the cumbersome process of iterative experiments can be eliminated directly by the mathematical derivation obtained from the iteration results. This research will explore the application of the D.O.R.T. theory in analyzing the scattering coefficient related to the signal refracting off the cracked plate, along with the affect of repositioning the signal at different angle in retrospect to the crack on the plate.
As one component of this simulation, the ANSYS finite element software is implemented to stimulate the plate structure and retrieve the signal transmitter. Writing MATLAB programs, processing applications along with outputting scattered patterns are inclusive with the signal analysis. The simulation is ran by emitting signals from a transducer on two plates, one with cracks and one without cracks, the signal is emitted and captured. These two sets of signals are subtracted in order to obtain the scattered signals refracted from the cracked plate. In the time domain the signals are convoluted, and in the frequency domain they are multiplied. Multiplying in the frequency domain is significantly simpler, so Fast Fourier Transform(FFT) is used to convert the signal from the time domain to the frequency domain. We are able to derive the frequency domain signal that is arranged in the transfer matrix by utilizing the D.O.R.T. theory. Then the transfer matrix is used to calculate the scattering coefficient.
Circular-shaped array transducers are used to calculate the various angles of the scattering coefficient, which we used to draw the scattered patterns. A characteristic chart is developed to differentiate the scattering characteristics of different size and shaped cracks. By this method to establish a calculation of the scattering coefficient in each direction. Wish this method applied in practice, and have a further contribution for non-destructive testing.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 V
圖目錄 VI
第一章 緒論 1
1-1 前言 1
1-2 研究動機 2
1-3 文獻回顧 3
1-4 研究概念以及目的 6
1-5 本文架構 9
第二章 基礎理論以及振動訊號分析 10
2-1時間反轉法理論(Theory of time reversal method, TRM) 10
2-2 疊代式反轉法理論(Iterative time reversal method, ITRM) 12
2-3時間反轉因子分解理論 (Decomposition of time reversal operator, D.O.R.T.) 15
2-4 Morlet wavelet 19
2-5平板之振動分析理論 22
2-6平板彎曲波之傳遞 25
第三章 參數設定與模擬分析 27
3-1 ANSYS有限元素模型參數之設定 28
3-2 發射訊號之設定 31
3-3 波群於模擬環境中之傳遞速度 32
第四章 散射幅射圖之結果與討論 35
4-1 陣列元件位置與計算散射係數之設定流程 39
4-2 圓孔裂縫散射之探討 45
4-3 矩形裂縫散射之探討 51
4-4 訊號發射角度改變對於矩形裂縫之探討 66
第五章 結果討論與未來展望 69
5-1 結果討論 69
5-2 未來展望 71
參考文獻 72
附錄一 75

[1]C. Draeger, D. Cassereau and M. Fink,(Sep 1997) “Theory of the Time Reversal Process in Solids, J.A.S.A., pp.1289-1295.
[2]C. Prada, J. Thomas, and M. Fink,(Jan 1995) “The iterative time reversal process: Analysis of the convergence, J. A. S. A., Vol.97, No.1, 62-71.
[3]C. Prada, M. Tanter, and M. Fink,(Oct 1997)“Flaw detection in solid with the D.O.R.T. method, IEEE Ultrasonic Symposium Proceedings, 679-683.
[4]Don H. Johnson, Dan E. Dudgeon, “Array Signal Processing: Concepts and Techniques. P T R Prentice Hall, Englewood Cliffs, NJ 07632.
[5]E. Kerbrat, C. Prada, D. Cassereau, R.K. Ing and M. Fink, (2000)“Detection and imaging in complex media with the D.O.R.T. method, IEEE Ultrasonic Symposium Proceedings, 779-783.
[6]E. Kerbrat, C. Prada, D. Cassereau, and M. Fink,(Mar 2003) “Image in the presence of grain noise using the decomposition of the time reversal operator. J. A. S. A., Vol.113, No.3, 1230-1240.
[7]E. Kerbrat, R.K. Ing, C. Prada, D. Cassereau, and M. Fink,(Mar 2003) “The D.O.R.T. method applied to detection and imaging in plates using Lamb waves, AIP Conf. Proceedings, 934-940.
[8]E. Kerbrat, D. Clorennec, C. Prada, D. Royer, D. Cassereau, and M. Fink,(May 2002) “Detection of cracks in a thin air-filled hollow cylinder by application of the DORT method to elastic components of the echo, Ultrasonics, Vol.40, No.1-8, 715-720.
[9]H. C. Song, W. A. Kuperman, and W. S. Hodgkiss,(Jun 1999)“Iterative time reversal in the ocean, J. A. S. A., Vol.105, No.6, 3176-3184.
[10]H. Sohn, H. W. Park, K. H. Law and C. R. Farrar,(July 2007)“Damage Detection in Composite Plates by Using an Enhanced Time Reversal Method , Journal of Aerospace Engineering, Vol.20, issue 3, pp.141-151.
[11]M. Fink,(1993) “Time-Reversal Mirrors, J. Phys, D Appl, Phys, Vol.26, pp.1135-1142.
[12]M. Fink, (March, 1997)“Time-reversal Acoustics, Physics Today, pp.34-39.
[13]M. Fink et al., (1989)“Self-Focusing in Inhomogeneous Media with Time Reversal Acoustic Mirror, IEEE Ultrasonic Symposium. Proc., pp.681-686.
[14]J. S. Kim, H. C. Song, and W. A. Kuperman, (2001, May)“Adaptive time-reversal mirror, J. A. S. A., Vol.109, No.5, 1817-1825.
[15]K. G. Sabra, P. Roux, H. C. Song, W. S. Hodgkiss, and W. A. Kuperman,(Sep 2006) “Experimental demonstration of iterative time-reversed reverberation focusing in a rough waveguide. Application to target detection, J. A. S. A., Vol.120, No.3, 1305-1314.
[16]Prada, C., Manneville, S., Spoliansky, D., ＆ Fink, M.(1996) Decomposition of the time reversal operator: Detection and selective focusing on two scatterers. The Journal of the Acoustical Society of America, 99, 2067.
[17]Wilcox, P. D., ＆ Velichko, A. (March 2010). Efficient finite element modeling of scattering for 2D and 3D problems. In SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring (pp. 76501E-76501E). International Society for Optics and Photonics.
[18]Yan, F., Royer, R. L., ＆ Rose, J. L. (2010). Ultrasonic guided wave imaging techniques in structural health monitoring. Journal of intelligent material systems and structures, 21(3), 377-384.
[19]Yu, L., ＆ Giurgiutiu, V. (2008). In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection. Ultrasonics, 48(2), 117-134.
[20]林明宏, “時間反轉陣列之聚焦解析度分析, 國立台灣大學工程科學及海洋工程學系碩士論文, 中華民國九十五年.
[21]林聖哲, “應用時間反轉法與微麥克風陣列於手機裝置之抗噪技術研究,國立成功大學系統及船舶機電工程學系碩士論文, 中華民國九十七年.
[22]吳柏賢. (2010). 麥克風陣列訊號處理於聲源訊號分離與聲場重建之應用研究. 成功大學系統及船舶機電工程學系碩博士班學位論文, (2010 年), 1-72.
[23]黃怡中, “應用時間反轉法聚焦蘭姆波於缺陷檢測,國立中山大學機械與機電工程學系碩士論文, 中華民國九十八年.
[24]楊澤民, 涂季平, 黃彥叡, ＆ 陳志文. (2011). 時間反轉法應用於平板裂縫偵測. 中國造船暨輪機工程學刊, 30(1), 31-42。
[25]楊澤民, 涂季平, 陳志文, ＆ 曾建銘. (2011). 散射路徑在平板裂縫偵測之分析研究.中國造船暨輪機工程學刊, 30(3), 52-65。
[26]李輝煌, “ANSYS工程分析基礎與觀念,高立出版社, 中華民國九十八年。
[27]陳永增、鄧惠源著，“非破壞檢測，全華科技圖書股份有限公司，89年10月。