雙層壓電複合材料受機電點載荷之暫態波傳問題

Transient Elastic Waves Propagating in a Two-Layered Piezoelectric Medium Subjected to the Mechanical and Electrical Concentrated Loadings

黃國書(Kuo-Shu Huang)

指導教授 ： 應宜雄

淡江大學/工學院/航空太空工程學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00030

摘要

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。

關鍵字

壓電 ； 複合層板 ； 反平面 ； 機電點載荷 ； 電位移

並列摘要

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.

並列關鍵字

Piezoelectric, Bimaterials ； Anti-plane ； Concentrated loadings ； Electric displacement

參考文獻

廖雪吩 (2007)，應用數值拉普拉斯逆轉換法於壓電材料動力破壞之研究，淡江大學航空太空工程學系碩士班碩士論文。

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Dubner, H. and Abate, J., (1968) “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform,” Journal of the Association for Computing Machinery 15, 115–123.

Durbin, F., (1974) “Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method,” The Computer Journal 17, 371–376.