請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43914
標題: | 具週期性電極之壓電薄膜阻抗分析 Impedance Analysis of Piezoelectric Film with Periodic Electrodes |
作者: | Yi-I-Che Tseng 曾一哲 |
指導教授: | 周元昉 |
關鍵字: | Floquet定理,平面波展開法,Stroh法,頻散曲線,阻抗分析,慢度關係式, Floquet theory,plane wave expansion method,Stroh formalism,dispersion relation,impedance analysis,slowness relation, |
出版年 : | 2009 |
學位: | 碩士 |
摘要: | 本文提出一套矩陣架構的理論來解決具週期性電極的壓電波傳行為,其概念結合了平面波展開法與Stroh法兩種,並假設系統在電性準靜態的情形下作用,首先由壓電本構方程式出發並配合牛頓運動定律與高斯定律即可推得壓電統御方程式,再由Floquet定理將位移及電位假設為週期函數展開的形式來滿足週期性邊界,並將位移及電位假設代入壓電統御方程式中則可推得一特徵值問題,將所求的特徵值與特徵向量以不同待定係數疊加則可求得壓電材料的通解,而在邊界條件方面則利用一次近似法來考慮週期性電極厚度所造成的影響,並求得電極在開路與短路兩種情形下之頻散關係式,此外亦討論指叉電極的阻抗與角頻率關係,在數值方面本文詳細介紹了壓電波傳的無因次化方法,並介紹頻散關係函數的連續化方法,如此則可快速的求得頻散曲線,而本文還利用慢度與特徵值的關係來判別在不同情形下的波傳特性。 This thesis bring up with a matrix-structured theorem to solve the wave propagation problem in piezoelectric material with periodic electrode distribution which combines plane wave expansion method and Stroh formalism. Starting with piezoelectric constitutive equation, governing equation can be derived from Newton’s motion equation and Gauss’s law. Then presuming that displacement and electrical potential are periodic function with the concept of Floquet theory. An eigen-value problem is obtained after substituting the assumed field into governing equation. Summing all eigen-vector of corresponding eigen-value with different coefficient to be determined to fulfill the general solution in the piezoelectric domain. The boundary condition of the electrode patch is represented by first order approximation of the electrode thickness. The dispersion relation of both open and short circuit is presented. The relation between impedance and frequency is also discussed. On the numerical, this thesis introduces a non-dimensionlize to the detail. And a quick approach to the dispersion relation using a method to continualize the dispersion function is introduced. Besides, this thesis differentiate the wave-propagate property of different situation with slowness and eigen-value. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43914 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
ntu-98-1.pdf 目前未授權公開取用 | 5.06 MB | Adobe PDF |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。