本文應用模態分析配合應變能法(SEM)針對複合材料疊層板之表面與基材裂縫進行非破壞檢測。複合材料採用碳纖維/聚二醚酮(AS4/PEEK)製造成 、 、 與 等疊層板。表面裂縫與基材裂縫分別以雷射切割與拉伸試驗產生。首先，應用有限元素分析軟體(ANSYS)建立疊層板破壞前後之有限元模型，進行模態分析以獲得破壞前後疊層板之自然頻率與模態振型。實驗模態分析則以衝擊鎚為驅動器、加速度計為感測器，針對疊層板破壞前後進行模態實驗，求取結構模態參數。經由比對分析與實驗之模態參數，確認有限元模型之等效性。最後，將破壞前後之模態振型以應變能法定義一破壞指標用來預測破壞的位置。其中，應變能之計算採用微分值積法(DQM)。結果顯示，分析與實驗之破壞指標均可成功地預測出複合材料疊層板之表面與基材裂縫位置。

The work presents an approach to detect surface crack and matrix cracking in composite laminates by using modal analysis and strain energy method (SEM). Carbon/epoxy composite AS4/PEEK was used to fabricate laminated plates, 、 、 and . Two types of damages, surface crack and matrix cracking, were investigated in this study. Surface crack damage was created on one side of the plate using a laser cutting machine. Matrix cracking in 90-degree lamina was created by subjecting to tensile test. A CAE software, ANSYS, was used to create finite element model for laminated plates. Normal mode analysis was performed to obtain the natural frequencies and the associated mode shapes. Experimental modal analysis (EMA) was also carried out using impact hammer and accelerometer to obtain modal parameters. Both FEA and EMA results were compared in order to validate FE model. The measured mode shapes were then used to compute the strain energy using differential quadrature method (DQM). A damage index was defined using the change of strain energy of the laminated plates before and after damage. Consequently, the damage index successfully located the surface crack and matrix cracking in the laminated plates. A pre-study was performed to access this approach by using a 3-D finite element analysis (FEA).

摘 要 I
Abstract II
誌 謝 IV
目 錄 V
表 目 錄 VIII
圖 目 錄 X
符號索引 XIII
第1章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.3 全文概述 5
第2章 有限元素分析 7
2.1 有限元素模型建立 7
2.1.1 材料參數設定 7
2.1.2 元素選用 8
2.1.3 網格劃分 9
2.1.4 邊界條件設定與分析求解 10
2.1.5 破壞模擬 10
2.2 收斂性分析 11
2.3 模型驗證 14
2.4 最佳化分析 15
第3章 實驗模態分析 16
3.1 複合材料疊層板之製作 16
3.2 模態實驗 18
3.2.1 實驗儀器選用 19
3.2.2 實驗條件 19
3.2.3 實驗步驟 21
3.2.4 曲線嵌合 22
3.3 破壞製作 23
3.4 裂縫位置確認 23
3.5 拉伸試驗 26
第4章 模型驗證 29
4.1 複合材料疊層板之模型驗證 29
4.1.1 疊層板之頻率響應函數驗證 29
4.1.1.1 疊層板 29
4.1.1.2 疊層板 33
4.1.1.3 疊層板 36
4.1.2 疊層板之模態參數驗證 39
4.1.2.1 疊層板 39
4.1.2.2 疊層板 45
4.1.2.3 疊層板 50
4.1.3 疊層板之模態保證指標驗證 58
4.1.3.1疊層板 之MAC驗證 58
4.1.3.2疊層板 之MAC驗證 61
4.1.3.3疊層板 之MAC驗證 63
4.2 複合材料疊層樑之模型驗證 65
4.2.1 疊層樑 之同點頻率響應函數驗證 65
4.2.2 疊層樑 之轉移頻率響應函數驗證 69
4.2.3 疊層樑 之模態參數驗證 72
4.2.4 疊層樑 之模態保證指標(MAC)驗證 83
4.2.4.1 試件1之MAC驗證 83
4.2.4.2 試件2之MAC驗證 85
4.3 模型驗證總結 87
第5章 破壞預測 89
5.1 複合材料疊層板之應變能 89
5.2 應變能破壞預測程序 94
5.2.1 應變能破壞預測程式架構 94
5.2.2 微分值積法 97
5.2.3 程式預測流程 99
5.3 破壞預測結果 101
5.3.1 表面裂縫預測 101
5.3.1.1 疊層板表面裂縫預測結果 101
5.3.1.2 疊層板表面裂縫預測結果 106
5.3.1.3 疊層板表面裂縫預測結果 110
5.3.2 基材裂縫預測 114
5.3.2.1 基材裂縫位於第13號格點之預測結果 114
5.3.2.2 基材裂縫位於第10號格點之預測結果 117
5.3.2.3 多條基材裂縫形成時之分析預測結果探討 120
5.3.2.4 基材裂縫在自由與懸臂邊界下之分析預測比較 122
5.4 破壞預測總結 124
第6章 結論與建議 126
參考文獻 128
附錄 複合材料疊層板材料參數圖 131
作者簡介 135

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