臺灣博碩士論文加值系統

本文探討以板波主動偵測平板圓孔及裂縫缺陷位置的技術及尺寸辨識的工作原理，並評估其檢測能力。利用黏貼於鋁合金平板之壓電陶瓷元件作為窄頻的板波致動器及 板波的感測器，並以小波轉換對於暫態板波訊號進行時頻域分析，由缺陷散射波波群的波程時間差與訊號分析鑑定缺陷位置及頻譜特徵。
含缺陷平板的板波訊號包括散射波訊號及壓電元件間直接波傳的板波訊號，在理想狀況下，含缺陷的板波訊號減去不含缺陷的板波訊號，可獲得自缺陷散射的板波訊號。本研究建立以簡單體法為基礎的尋優程式，反算平板缺陷的位置，所發展的缺陷定位目標函數具有唯一的全域極小值，可以保證缺陷定位計算的精確性，在實驗上已獲得良好的結果。散射波頻譜特徵與缺陷的種類、尺寸、波傳路徑、入射角度有關，裂縫尖端的繞射波訊號太小，裂縫尖端與壓電感測器之距離要足夠近，否則不易偵測裂縫尖端的繞射波。未來需發展散射波頻譜的相關數值分析，進一步比較實驗值與理論值，估算平板缺陷的尺寸。

This thesis experimentally investigates feasibility of detecting the locations and sizes of damages such as a circular hole and its edge crack in a plate using an active damage detection technology based on scattered plate waves. The experiments were carried out by an array of piezoelectric ceramic PZT discs surface mounted on both sides of the specimens as actuators and sensors to launch and detect the fundamental anti-symmetric plate waves. Damage positions are determined through time-of-flight of the envelop of wave group, which and the scattered spectra of plate waves from damages are characterized by time-frequency analysis. The time-frequency analysis on signals of plate wave was processed by continuous wavelet transform with a mother wavelet of Gaussian cosine pulse.
Besides scattered plate waves from the damages, the signals for the damaged plate also include the signals of plate wave propagating direct from actuators to sensors. Under only ideal conditions, the signals of scattered plate waves can be evaluated from the difference between those signals for damaged plates and undamaged plates. The location of damage area is determined using the simplex algorithm, in which the objective function is a summation of the square of time-of-flight differences among scattered waves and those waves direct propagating between actuators and sensors. It guarantees seeking the exact location of damage due to existence of only one global minimum for the specimens having a single damage. A very good agreement between experimental results and predictions was achieved. The characteristics of scattered spectra are found to be dependent on damage types, sizes, paths of wave propagation, and angle of incidence. It results in a critical need to develop a numerical analysis of scattered spectra for various damages as references to compare them with experimental results in the near future. The present method can detect damages such as circular holes in a large plate. However, it is difficult to detect edge cracks extending from circular holes since the diffracted plate waves decay fast from the crack tips, which are far away from the actuators and sensors in these specimens.

目 錄
頁次
中文摘要 i
英文摘要 ii
誌謝 iv目錄 v
圖表目錄 vii
第一章 緒論 1
1.1 研究背景 1
1.2 文獻回顧 2
1.3 內容簡述 4
第二章 板波的波傳 6
2.1 等向性平板的板波波導 6
2.2.1 藍姆波的相速度 6
2.2.2 藍姆波的群速度 8
第三章 實驗與分析 11
3.1 實驗及裝置 11
3.2 高頻訊號的時頻域分析 12
3.2.1 小波轉換分析 12
3.2.2 波群速度的量測 14
3.2.3 板波散射的頻譜特徵 14
3.3 圓洞缺陷位置反算模型 15
第四章 結果與討論 17
4.1圓孔缺陷散射波的波程時間分析 17
4.2 裂縫缺陷繞射波的波程時間分析 18
4.3 圓孔缺陷位置的鑑定 18
4.4 圓孔缺陷散射波頻譜的分析 19
第五章 結論與未來展望 21
5.1 結論 21
5.2 未來展望 22
參考文獻 24
附錄1 27
附錄2 29
附錄3 30
附表 31
附圖 39
圖表目錄
頁次
表1 6061鋁板之材料常數 31
表2 基本模態 板波的相速度與群速度 32
表3 試片一之 mm圓洞缺陷散射的波程時間差及誤差 33
表4 試片一之 mm圓洞缺陷散射的波程時間差及誤差 34
表 5 含 mm圓洞缺陷試片三之路徑1至2散射的
波程時間差及誤差 35
表 6 含 mm圓洞缺陷試片三之路徑2至3散射的
波程時間差及誤差 36
表 7 含 mm圓洞缺陷試片三之路徑1至4散射的
波程時間差及誤差 37
表 8 含 mm圓洞缺陷試片三之路徑3至4散射的
波程時間差及誤差 38
圖1 壓電材料的逆壓電效應 39
圖2 (a)對稱及(b)反對稱板波的致動與生成 39
圖3 高斯餘弦脈波激振函數曲線 40
圖4 圓孔缺陷散射波之訊號處理 41
圖 5 (a)對稱及(b)反對稱板波變位的示意圖 42
圖 6 波群波傳的示意圖 43
圖7 6061鋁板的 與 板波之頻散曲線 43
圖 8 含圓孔缺陷與裂縫之(a)試片一、(b)試片二及(c)試片三 44
圖9 平板缺陷主動偵測實驗裝置示意圖 45
圖10 含圓孔缺陷之平板試片及壓電換能器的實驗照片 46
圖11 實驗儀器的照片 46
圖12 高斯脈波母小波函數圖 47
圖13 板波群速度實驗與理論比較(實線代表理論值，
圓點代表實驗值) 48
圖 14 在含直徑10 mm圓孔之試片三上，波傳路徑1至4的散射波
頻譜計算程序示意圖 49
圖15 裂縫位置尋優之目標函數的(a)透視圖與(b)等高線圖 50
圖 16 在試片一(600´600 mm平板)上，波傳路徑為壓電換能器1至2
的(a)板波訊號及(b)小波轉換係數的包絡線 51
圖 17 在含直徑3 mm圓孔的試片一上，波傳路徑為壓電換能器1至
2的(a)板波訊號及(b)小波轉換係數的包絡線 52
圖 18 在含直徑5 mm圓孔的試片一上，波傳路徑為壓電換能器1至
2的(a)板波訊號及(b)小波轉換係數的包絡線 53
圖 19 在含直徑8 mm圓孔的試片一上，波傳路徑為壓電換能器1至
2的(a)板波訊號及(b)小波轉換係數的包絡線 54
圖 20 在含直徑10 mm圓孔的試片一上，波傳路徑為壓電換能器1
至2的(a)板波訊號及(b)小波轉換係數的包絡線 55
圖 21 在含直徑10 mm圓孔及長10 mm裂縫的試片一上，波傳路徑
為壓電換能器1至2的(a)板波訊號及(b)小波轉換係數的包絡
線 56
圖 22 在試片一上，波傳路徑為壓電換能器1至2的小波轉換係數的
包絡線之灰階圖(a)不含圓洞(b) 含直徑3 mm圓孔 57
圖 23 在試片一上，波傳路徑為壓電換能器1至2的小波轉換係數的
包絡線之灰階圖(a) 含直徑5 mm圓孔 (b) 含直徑8 mm圓孔 58
圖 24 在試片一上，波傳路徑為壓電換能器1至2的小波轉換係數的
包絡線之灰階圖(a) 含直徑10 mm圓孔 (b) 含直徑10 mm圓
孔及長10 mm裂縫 59
圖 25 在試片二(450´450 mm平板)上，波傳路徑為壓電換能器1至2
的(a)板波訊號及(b)小波轉換係數的包絡線 60
圖 26 與圖25同，惟波傳路徑為壓電換能器1至3 61
圖 27 與圖25同，惟波傳路徑為壓電換能器1至4 62
圖 28 與圖25同，惟波傳路徑為壓電換能器2至3 63
圖29 與圖25同，惟波傳路徑為壓電換能器2至4 64
圖30 與圖25同，惟波傳路徑為壓電換能器3至4 65
圖31 在含直徑10 mm圓孔的試片二上，波傳路徑為壓電換能器1
至2的(a)板波訊號及(b)小波轉換係數的包絡線 66
圖32 與圖31同，惟波傳路徑為壓電換能器1至3 67
圖33 與圖31同，惟波傳路徑為壓電換能器1至4 68
圖34 與圖31同，惟波傳路徑為壓電換能器2至3 69
圖35 與圖31同，惟波傳路徑為壓電換能器2至4 70
圖36 與圖31同，惟波傳路徑為壓電換能器3至4 71
圖37 在試片三(600´600 mm平板)上，波傳路徑為壓電換能器1至
2的(a)板波訊號及(b)小波轉換係數的包絡線 72
圖38 與圖37同，惟波傳路徑為壓電換能器1至3 73
圖39 與圖37同，惟波傳路徑為壓電換能器1至4 74
圖40 與圖37同，惟波傳路徑為壓電換能器2至3 75
圖41 與圖37同，惟波傳路徑為壓電換能器2至4 76
圖42 與圖37同，惟波傳路徑為壓電換能器3至4 77
圖43 在含直徑10 mm圓孔的試片三上，波傳路徑為壓電換能器1
至2的(a)板波訊號及(b)小波轉換係數的包絡線 78
圖44 與圖43同，惟波傳路徑為壓電換能器1至3 79
圖45 與圖43同，惟波傳路徑為壓電換能器1至4 80
圖46 與圖43同，惟波傳路徑為壓電換能器2至3 81
圖47 與圖43同，惟波傳路徑為壓電換能器2至4 82
圖48 與圖43同，惟波傳路徑為壓電換能器3至4 83
圖49 不同波傳路徑之散射波頻譜實驗值(實心圓圈表直徑5 mm圓
孔，實心三角表直徑10 mm圓孔) 84
圖50 不同波傳路徑之散射波頻譜實驗值對於 的變化圖(實心圓
圈表直徑5 mm圓孔，實心三角表直徑10 mm圓孔) 85

1. F. L. Degertekin and B. T. Khuri-Yakub (1996), ”Single mode Lamb wave excitation in thin plate,” Applied Physics Letters, 69(2), 146-148.
2. F. L. Degertekin and B. T. Khuri-Yakub (1996), “Hertzian contact transducers for nondestructive evaluation,” Journal of the Acoustical Society of America, 99(1), 299-308.
3. E. Moulin, J. Assaad and C. Delebarre (1997), ”Piezoelectric transducer embedded in a composite plate: Application to Lamb wave,” J. Appl. Phys., 82(5), 2049-2055.
4. C. A. Paget and K. Levin (1999), “Structural integrity of composites with embedded piezoelectric ceramic transducer,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3668, 306-313.
5. C. A. Paget, K. Levin and C. Delebarre (2000), “Behavior of an embedded piezoceramic transducer for Lamb wave generation in mechanical loading,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3985, 510-520.
6. H. T. Banks, D. J. Inman, D. J. Leo and Y. Wang (1996), “An experimentally validated damage detection theory in smart structure,“ Journal of Sound and Vibration, 191(5), 859-880.
7. Z. Jiang, K. Kabeya and S. Chonan (1999), “Longitudinal wave propagation measuring technique for structural health monitoring,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3668, 343-350.
8. S. Beard and F.-K. Chang (1997), “Active damage detection in filament wound composite tubes using built-In sensors and actuator,” Journal of Intelligent Material Systems and Structures, 8, 891-897.
9. Youn—Seo Roh (1998), “Built —in diagnostics for identifying an anomaly in a plate using wave scatter,” Ph.D. Dissertation, Stanford University.
10. S. Grondel, E. Moulin, C. Delebarre (1999), “Lamb wave assessment of fatigue damage in aluminum plates,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3668, 371-381.
11. A. Gachagan, G. Hayward, A. McNab, P. Reynolds, S. G. Pierce, W. R. Phlip and B. Culshaw (1999), “Generation and reception of ultrasonic guided waves in composite plates using conformable piezoelectric transmitters and optical-fiber Detectors,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 46(1), 72-81.
12. P. F. Pai and S. Jin (2000), “Locating structural damage using operational deflection shapes,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3985, 271-282.
13. S. Grondel, C. Delebarre and J. Assaad (2001), “Modelling of Lamb wave generation for application in health monitoring of composite plates,” IEEE Ultrasonics Symposium, 721-724.
14. S. S. Kessler (2002), “Piezoelecric-based in-suit damage detection of composite material for structural health monitoring systems,” Ph.D. Thesis, Aeronautics and Astronautics at the Massachusetts Institute of Technology.
15. M. S. Caceci and W. P. Cacheris (1984), “Fitting curves to data: the simplex algorithm is the answer,” Byte, 340-362.
16. A. Abbate, J. Frankel and P. Das(1995), “Wavelet transform signal processing for dispersion analysis of ultrasonic signals,” IEEE Ultrasonics Symposium, 751-755.
17. C. Boller, C. Biemans, W. J. Staszewski, K. Worden, G. R. Tomlinson (1999), “Structural damage monitoring based on an actuator-sensor system,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3668, 285-294.
18. R. E. Seydel and F. K. Chang (1999), “Real-time impact identifiction of stiffened composite panels,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3668, 295-305.
19. V. Giurgiutiu, J. Redmond, D. Roach and K. Rackow (2000), “Active sensor for health monitoring of aging aerospace structures,” Proceeding of the SPIE Conference on Smart Structures and Integrated Systems, 3985, 294-305.
20. S. Grondel, J. Assaad, C. Delebarre, J. P. Dupuis, L.Reithler (2000), “Study of fatigue crack in riveted plate by acoustic emission and Lamb wave analysis,” IEEE Ultrasonics Symposium, 805-808.
21.蘇逢奇(1997)，小波轉換在有限尺寸平板音洩源定位研究之應用， 國立交通大學機械工程學系碩士論文，台灣，新竹市。