本文乃解析雙異質壓電複合層板承受反平面動力點載荷及平面電位移點載荷時之暫態波傳問題，此複合材料為由兩層不同厚度之壓電材料所構成的雙層複合條板。解析時，首先利用單邊與雙邊拉普拉斯積分轉換法求得兩次轉換域中的剪應力與電位移全場解，再利用Durbin單邊拉普拉斯數值逆轉換法以及延伸的雙邊拉普拉斯數值逆轉換法來求得暫態時域解。數值結果部分則針對不同觀察點位置、不同材料厚度比以及不同負載形式等情況作詳細計算與討論，並將本研究的特例與文獻上之雙層等厚板的靜力解作比較，以驗證本文數值結果的正確性。

In this study, transient elastic waves propagating in a two-layered piezoelectric medium subjected to anti-plane concentrated loading and in-plane electric displacement loading on the upper and lower free surfaces are investigated. The double-layer composite is constructed of two layers of piezoelectric materials with different thicknesses. The one-sided and the two-sided Laplace transforms are applied to obtain the shear stresses and the electric displacements in the transform domain. And then, the Durbin’s method for one-sided Laplace transform inversion and the extended Durbin’s method for two-sided Laplace transform inversion are used to carry out the numerical inversions. The numerical results for different field points, different ratios of thicknesses and different loading types are evaluated and discussed in detail.

中文摘要..........................................................................................I
英文摘要.........................................................................................II
目錄..........................................................................................................III
圖目錄......................................................................................................V
表目錄.....................................................................................................IX
第一章 緒論............................................................................1
1.1 研究動機............................................................................1
1.2文獻回顧............................................................................4
1.3內容簡介............................................................................10
第二章 理論基礎............................................................................12
      2.1  線性壓電材料控制方程式與本構方程式...............12
      2.2  拉普拉斯轉換及逆轉換................................................14
      2.3  Durbin方法.........................................................................15
      2.4  簡單數值範例.....................................................................17
      2.5 半無窮域壓電材料受反平面動力點載荷之暫態響  應..........................................................................................21
          2.5.1 半無窮域壓電材料受反平面動力點載荷之解析....21
          2.5.2 數值結果與比較........................................................26
第三章 雙異質壓電複合層板之暫態波傳解析...........................27
3.1  問題描述............................................................................27
3.2  雙異質壓電複合層板受反平面動力點載荷之解析......................................................................................29
3.3  雙異質壓電等厚層板受反平面動力點載荷之靜力解析.......................................................................................37
第四章  數值結果與討論............................................................40
    4.1 數值計算說明.......................................................................40
  4.2 數值結果與討論...................................................................41
第五章  結論與成果............................................................48
5.1 本文結論...............................................................................48
  5.2 本文成果...............................................................................49
5.3 尚待研究的方向...................................................................50
參考文獻..........................................................................................52
附錄一 論文簡要版................................................................................93








圖 目 錄
圖2-1  於雙重數值拉普拉斯逆轉換的方法在不同 之比較.............................................................58
圖2-2  於雙重數值拉普拉斯逆轉換的方法在相同 ，不同 之比較.............................................59
圖 2-3 於雙重數值拉普拉斯逆轉換的方法在相同 ，不同 之比較.............................................60
圖 2-4  於雙重數值拉普拉斯逆轉換的方法在相同 ，不同 之比較................................................61
圖 2-5半無窮域壓電材料受反平面動力點載荷之結構示意圖..........62
圖2-6 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉  斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................63
圖2-7 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................64
圖2-8 半無窮域壓電材料受反平面動力點載荷利用雙重數值拉普拉斯逆轉換與Cagniard-de Hoop method逆轉換於 觀察點位置所得到 數值解之比較............................................65
圖3-1雙異質壓電複合層板受反平面動力點載荷與平面電位    移點載荷負載之圖形...........................................................66
圖 3-2 雙異質壓電等厚層板受載荷作用之圖形.......................67
圖3-3 雙異質壓電等厚層板的兩負載所產生的應力場疊加之示意圖............................................................................68
圖4-1觀察點在(0,0)位置的剪應力 之暫態數值解與靜力解比較................................................................................................69
圖4-2 觀察點在 位置的剪應力 之暫態數值解與靜力解               比較...............………………………...…………………………70
圖4-3 觀察點在 位置的剪應力 之暫態數值解與靜力 解比較.................………………………………...……...………71
圖4-4 觀察點在 位置的剪應力 之暫態數值解與靜力解 比較.................…………………………………......………....…72
圖4-5 觀察點在 位置的剪應力 之暫態數值解與靜力解比較.................……………………………………...…...…....…....73
圖4-6觀察點在(0,0)位置於長時間的剪應力 之暫態數值圖.........74
圖4-7觀察點在(0,0)位置的剪應力 之暫態數值圖............................75
圖4-8觀察點在 之不同位置的剪應力 之暫態數值圖....76


圖 4-9 觀察點在 之不同位置的剪應力 之暫態數值圖..........77
圖 4-10觀察點在 之不同位置的剪應力 之暫態數值圖..78
圖 4-11觀察點在 之不同位置僅施加電位移負載的剪應力 之暫態數值圖..........................................................………....…....79
圖4-12 觀察點在 之不同位置僅施加電位移負載的剪應力 之暫態數值圖.............………………………........………....…....80
圖4-13觀察點在 之不同位置僅施加電位移負載的剪應力    之暫態數值圖..................................................................................81
圖 4-14 觀察點在(0,0)位置雙層材料之不同厚度比的剪應力 之暫態數值圖.................…………………………………....….........82
圖 4-15 觀察點在(0,0)位置雙層材料之不同厚度比的剪應力 之暫態數值圖...........................………………………………....…....83
圖4-16觀察點在(0,0)位置雙層材料之不同厚度比僅施加電位移負載的剪應力 之暫態數值圖......…………….....………....…....84
圖 4-17 觀察點在(0,0)位置施加不同電位移負載大小的剪應力 之暫態數值圖.................……………….....………………....…....85
圖 4-18 觀察點在 之不同位置的電位移 之暫態數值圖.......
         ....................................................................................................................86
圖 4-19 觀察點在 之不同位置的電位移 之暫態數值圖.............
         ....................................................................................................................87
圖 4-20 觀察點在 之不同位置的電位移 之暫態數值圖....
         ....................................................................................................................88
圖 4-21 觀察點在(0,0)位置雙層材料之不同厚度比的電位移 之暫    態數值圖.................……………….....………………....…........89
圖4-22 觀察點在(0,0)位置施加不同機械應力大小的電位移 之暫態數值圖.................……………….....………………....…........90
圖4-23 觀察點在 位置雙層材料之不同厚度比施加機械應力產生頭前波效應的 之暫態數值圖...........................…....91
表 目 錄
表4-1 壓電常數表……………………………………………………..92

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