臺灣博碩士論文加值系統

本文主要探討基於振動方法於結構非破壞檢測之評估。主要運用有限元素分析及實驗模態分析，對一具破壞之自由邊界板進行非破壞檢測，應用位移振型差法、位移振型差斜率法及應變能法三種破壞預測方法，發展出一套自動化破壞檢測程式，進而找出破壞的位置。首先，進行有無破壞自由邊界板之模型驗證，根據理論得到自由邊界板之理論模態參數，接著應用有限元素分析求得有無破壞板結構之自然頻率、模態振型及頻率響應函數；接著利用傳統實驗模態分析方法，以衝擊鎚為驅動器、加速度計為感測計之方式分別對有無破壞板結構進行實驗，進而得到實驗結構板之模態參數，包括自然頻率、模態振型及阻尼比。最後，比較有無破壞板之模態參數，以完成模型驗證。其次，由數值分析在不同破壞深度、不同破壞位置、兩破壞同時發生及斜方向破壞四種情形，三種破壞預測程式均能找到實際之破壞位置。最後，舉一實際例子，三種破壞預測程式能找到破壞可能發生之位置。本文說明了應用實際量測之位移振型作為破壞預測可行性。

This work presents the evaluation of vibration-based method for structural nondestructive inspection. The finite element analysis (FEA) and the experimental modal analysis (EMA) are applied to a defected free-free plate for structural nondestructive inspection. Three faults defection program are developed to find the defected location based on the change of the mode shape difference method, the slope of mode shape difference method and the strain energy method. First, the structural model verification of both defected and undefected free-free plate is performed. The system modal parameters, including natural frequencies, mode shapes and frequency response function (FRF) can theoretically be determined by FEA. The conventional EMA is also carried out with the use of the impact hammer and accelerometer to obtain FRF as well as the modal paramaters. Both the FEA and EMA results as well as the theoretical solution from the literature are compared and verified. The modal parameters agree reasonably well. Numerical analysis to predict the defected(crack) location is also shown for the case of different crack depth, different crack locations, two cracks and skew cracks. The three faults defection program can reasonably predict the defected area for all cases. This work enhances the vibration-based method for fault diagnosis by utilizing the structural mode shapes.

目 錄
摘要 I
英文摘要 II
誌謝 III
目錄 IV
圖目錄 VII
表目錄 XI
第一章 緒論……………………………………………………...1
1.1 研究動機………………………………………………….1
1.2 文獻回顧………………………………………………….3
1.3 研究目的………………………………………………….7
1.4 全文概述………………………………………………….8
第二章 自由邊界板之模型驗證……………………………….10
2.1 模型驗證之流程圖………………………………………12
2.2 自由邊界板之理論分析…………………………………13
2.3 自由邊界板之有限元素分析…………………………....15
2.3.1 無破壞板之有限元素分析……………………….15
2.3.2 破壞板之有限元素分析………………………….17
2.4 自由邊界板之實驗模態分析……………………………19
2.4.1 無破壞板之實驗模態分析……………………….19
2.4.2 破壞板之實驗模態分析………………………….21
2.5 結果與討論………………………………………………23
2.5.1 無破壞板之模型驗證…………………………….23
2.5.2 破壞板之模型驗證……………………………….36
2.6 結論………………………………………………………45
第三章 破壞預測方法之介紹……………………………….…47
3.1 破壞預測方法之介紹……………………………………48
3.1.1 位移振型差法…………………………………….48
3.1.2 位移振型差斜率法……………………………….50
3.1.3 應變能法………………………………………….51
3.1.4 微分值積法……………………………………….55
3.2 破壞預測方法之程式流程圖…………………………...60
3.2.1 振型差法………………………………………….60
3.2.2 振型差斜率法…………………………………….61
3.2.3 應變能法………………………………………….62
3.3 結論……………………………………………………...67
第四章 破壞預測結果與討論………………………….….…..68
4.1 有限元素分析破壞預測之結果…………………………69
4.1.1不同破壞深度之預測……………………………..69
4.1.2 不同破壞位置之之預測………………………….76
4.1.3 兩破壞同時發生之預測………………………….82
4.1.4 斜破壞之預測…………………………………….87
4.2 實驗模態分析破壞預測之結果………………………...92
4.3 結論……………………………………………………...96
第五章 結論與建議………………………………………...…..98
5.1 結論……………………………………………………..98
5.2 建議……………………………………………………..99
參考文獻………………………………………………………...102
符號索引………………………………………………………..111
附錄A：其它不同破壞深度之預測結果……………………... 113
附錄B：其它不同破壞位置之預測結果……………………... 119
附錄C：其它兩個破壞同時發生之預測結果………………... 124
附錄D：其它斜破壞之預測結果……………………………... 129
附錄E：L形、斜中心破壞之預測結果……………………… 134
作者簡介………………………………………………………...136
圖目錄
圖2-1 模型驗證之流程圖………………………..…………….12
圖2-2 四邊自由邊界板之實際狀況……..…………………….15
圖2-3 無破壞自由邊界板之有限元素分割情形……..……….17
圖2-4 實際破壞之自由邊界板情形…………………………...18
圖2-5 破壞自由邊界板之有限元素模型……………………...18
圖2-6 實驗架構圖……………………………………………...20
圖2-7 實際實驗情形圖………………………………………...20
圖2-8 無破壞板之分割及編號情形…………………………...21
圖2-9 破壞板之加工情形……………………………………...22
圖2-10 無破壞板之實驗與理論頻率響應函數比較圖………...24
圖2-11 無破壞板之關聯性函數圖……………………………...26
圖2-12 破壞板之實驗與理論頻率響應函數比較圖…………...36
圖2-13 破壞板之關聯性函數圖形……………………………...38
圖3-1 自由邊界板在有無破壞情形下之振型圖(mode 1)…….48
圖3-2 x方向及y方向之振型差變化情形…..…………………49
圖3-3 程式架構流程...…..…………………..…………..63
圖4-1實際不同破壞深度之情形……..………………….70
圖4-2不同破壞深度預測之結果圖(Lx=2.4cm)……..…………73
圖4-3不同破壞深度預測之結果圖(Lx =4.8cm)………..………74
圖4-4不同破壞深度預測之結果圖(Lx =7.2cm)………………..75
圖4-5實際不同破壞位置之情..……….………………..…76
圖4-6不同破壞位置預測之結果圖(y=4.8cm)…………………79
圖4-7不同破壞位置預測之結果圖(y=9.6cm)…………………80
圖4-8不同破壞位置預測之結果圖(y=14.4cm)………………..81
圖4-9實際兩破壞同時發生之情形………………………….…82
圖4-10 兩個破壞同時發生預測之結果圖
(x=7.2cm, Ly=4.8cm；y=9.6, Lx=7.2cm)……………...85
圖4-11 兩個破壞同時發生預測之結果圖
(x=21.6cm, Ly=4.8cm；y=9.6, Lx=7.2cm)…….………86
圖4-12 實際斜破壞之情形……………………………………...87
圖4-13 斜方向破壞預測之結果圖(x=6cm, Lx=6cm, Ly=6cm)....90
圖4-14 斜方向破壞預測之結果圖(x=18cm, Lx=6cm, Ly=6cm)..91
圖4-15 實際板子破壞之情形…………………………………...92
圖4-16 預測實驗破壞之結果圖(y=9.6cm, Lx=7.2cm)………….95
圖A-1實際不同破壞深度之情形……………………....113
圖A-2 Case x3 - Ly1 ……………………………………………...114
圖A-3 Case x3 - Ly2………………………………………………114
圖A-4 Case x3 - Ly3……………………………………………....115
圖A-5 Case x3 - Ly4………………………………………………115
圖A-6 Case y3 - Lx1………………………………………………116
圖A-7 Case y3 - Lx2………………………………………………116
圖A-8 Case y3 - Lx3………………………………………………117
圖A-9 Case y3 - Lx4………………………………………………117
圖A-10 Case y3 - Lx5……………………………………………..118
圖A-11 Case y3 - Lx6……………………………………………..118
圖B-1 實際不同破壞位置之情形………………….…....119
圖B-2 Case x1 - Ly4………………………………….…………...120
圖B-3 Case x2 - Ly4………………………………………………120
圖B-4 Case x3 - Ly4……………………………………….……...121
圖B-5 Case x4 — Ly4……………………………………….……..121
圖B-6 Case y1 - Lx5……………………….…………….….….…122
圖B-7 Case y2 - Lx5………………………….………….….….…122
圖B-8 Case y3 - Lx5………………………….…………….……..123
圖B-9 Case y4 - Lx5………………………………………..……..123
圖C-1實際兩破壞同時發生之情形…………………………..124
圖C-2 Case x2 - y1……………………………………...………..125
圖C-3 Case x2 - y2………………………………………...……..125
圖C-4 Case x2 - y3……………………………………….………126
圖C-5 Case x2 - y4…………………………………………….…126
圖C-6 Case y4 - x1………………………………………….……127
圖C-7 Case y4 - x2……………………………………….………127
圖C-8 Case y4 - x3…………………………………………….…128
圖C-9 Case y4 - x4…………………………………………….…128
圖D-1實際斜破壞之情形………………………….…………...129
圖D-2 Case x1(左下右上)…………………………..…….……..130
圖D-3 Case x3(左下右上)……………………………….…..…..130
圖D-4 Case x5(左下右上)……………………………….………131
圖D-5 Case x2(左上右下)……………………………….………131
圖D-6 Case x3(左上右下)……………………………….………132
圖D-7 Case x4(左上右下)………………………………...……..132
圖D-8 Case x5(左上右下)……………...………………..………133
圖D-9 Case x6(左上右下)……………………………….………133
圖E-1實際L形、斜中心斜破壞之情形………….………….134
圖E-2 Case L形破壞……………………………………………135
圖E-3 Case斜中心破壞……………………….………………..135
表目錄
表2-1 模態指標(i,j)尺寸參數表(a/b=1.5)………………….14
表2-2 自由邊界板之材料性質表……………………………...16
表2-3 無破壞板之理論自然頻率表…………………………...27
表2-4 四種元素之分析性質表………………………………...28
表2-5 各元素與無破壞板之理論自然頻率誤差百分比表…...29
表2-6 無破壞板之FEA(SHELL63)自然頻率表………………29
表2-7 無破壞板之FEA與EMA自然頻率誤差百分比……….30
表2-8 無破壞板之阻尼比誤差百分比(%)…………………….31
表2-9 無破壞板之FEA與EMA模態振型比較對照表……….32
表2-10 無破壞板之實驗振型與理論振型之MAC……………..35
表2-11 無破壞板之實驗振型與理論振型之MSF..…………….35
表2-12 破壞板之自然頻率誤差百分比………………………...39
表2-13 破壞板之阻尼比誤差百分比(%)……………………….40
表2-14 破壞板之FEA與EMA模態振型比較對照表…….……41
表2-15 破壞板之實驗振型與理論振型之MAC………………..44
表2-16 破壞板之實驗振型與理論振型之MSF………………...44
表A-1 其它不同破壞深度之情形表…………………………..113
表B-1 其它不同破壞位置之情形表…………………………..119
表C-1 其它兩個破壞同時發生之情形表……………………..124
表D-1 其它斜破壞之情形表…………………………………..129
表E-1 L形、斜中心破壞之情形表……………………………134

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