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標題: | 鋰酸鈮與等向性材料介面波之研究 Research on Interfacial Wave of Lithium Niobate and Isotropic Media |
作者: | Chi-Hsin Wang 王祈欣 |
指導教授: | 周元昉 |
關鍵字: | 介面波,拉普拉斯,鋰酸鈮, interfacial wave,sroneley wave,laplace,lithium niobate, |
出版年 : | 2009 |
學位: | 碩士 |
摘要: | 本文為探討介面波的存在範圍,提出一套以拉普拉斯轉換求解半無窮域波傳問題的方法,將問題簡化為只有一個特徵值問題,降低以電腦進行數值運算上的難度。
首先對於兩個半無窮域的統御方程式對深度方向進行拉普拉斯轉換,再以介面上的邊界條件作為待定係數代入,在兩個材料間建立起關係,並分別求得兩材料內轉換後的位移場及電位場,以拉普拉斯反轉換將其轉換為空間的位移場及電位場,最終由判斷位移場及電位場是否會發散來取得介面波存在的條件而得出介面波問題的速度方程式。 為證明此法的適用性,首先以前述方法求得等向性材料的介面波速度方程式,其結果與前人所得相同無誤。再以拉普拉斯轉換法求取立方晶系材料間及鋰酸鈮壓電晶體與等向性材料間的介面波存在範圍,以討論材料參數對於存再犯為的影響。 This thesis brings up a method to solve the wave propagating problem in semi-infinite medium based on Laplace transform. The treatment simplifies the problem, and become a single eigen-value problem to lower the difficulty on numerical processes. The Laplace transform in thickness direction coordinate is applied to the governing equation at both sides of the interface firstly. Then substitute the boundary conditions which relate the two semi-infinite mediums as undetermined coefficients in the transformed governing equation. The displacement field and electrical potential field in transformed domain in both side of interface are them obtained, an inverse transform applied to which after that result in the displacement field and electrical potential field in the untransformed space. Afterward, a judgment of whether the field convergence at infinite, which is the existence condition of the interfacial wave is executed, deriving the velocity function of the interfacial wave propagating problem. To verify the validity of this process, the method above is used to compute the velocity function of interfacial wave for isotropic material. It comes out to be identical with that already done by other scholars. The Laplace transform method is then carried out to solve the existence range of interfacial wave among cubic cubic interface and isotropic interface to discuss the influence of material constants on the existence range of interfacial wave. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45585 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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