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研究生: 陳志遠
Chen, Jhih-Yuan
論文名稱: 異向性平板頻散曲線初步探討
Preliminary investigations of dispersion curve of an anisotropic plate
指導教授: 宋見春
Sung, J.C.
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 55
中文關鍵詞: 異向性材料頻散方程式頻散曲線
外文關鍵詞: anisotropic materials, dispersion equations, dispersion curve
相關次數: 點閱:121下載:1
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  • 本文探討彈性波在異向性平板材料中傳播之行為,由彈性波在異向
    性材料中傳播應滿足的運動方程式、應力-應變及位移-應變關係條件,
    推演波在一般異向性平板材料中的頻散方程式。文中首先針對上下表面
    邊界條件曳引力全為零或位移全為固定之問題,推演頻散方程式並對頻
    散曲線求解的一些問題進行討論。其次推演多種不同邊界條件(無應力、
    位移固定、滑動)下的頻散方程式,繪製了不同材料在不同邊界條件下的
    頻散曲線圖並對結果加以討論。

    This article investigates the behavior of the propagation of elastic waves in anisotropic materials. By employing the elastic waves propagation in anisotropic materials which satisfy the equation of motion, stress-strain and displacement-strain relations, we briefly outline the derivation of dispersion equations for general anisotropic materials.
    We first focuse on the problem of dispersion curves for a plate with a totally traction-free or totally rigid boundary conditions on the upper and lower surfaces of plate. Next, we investigate the problem of dispersion curves for various boundary conditions (traction-free, rigid, slippery) prescribed on the surfaces of the plate. Numerical results are presented for different types of materials and results are discussed.

    摘要 I SUMMARY II 誌謝 VI 目錄 VII 圖目錄 IX 表目錄 XII 第一章 緒論 1 1.1前言 1 1.2文獻回顧 1 1.3本文綱要 3 第二章 基本公式 5 2.1基本公式建立 5 2.2上下表面邊界為無應力狀態 9 2.3上下表面邊界為位移固定狀態 14 第三章 層狀介質頻散方程式的推演 18 3.1 基本公式 18 3.2 傳遞矩陣E 20 3.3 不同邊界條件的頻散方程式 21 第四章 結果與討論 23 4.1 等向性材料的驗證 23 4.1.1 上下表面無應力之狀態 24 4.1.2 上下表面位移固定之狀態 32 4.2 特殊材料之結果 35 4.3 上表面無應力下表面位移固定狀態 41 4.4 表面滑動狀態 45 4.5 數值結果 50 第五章 結論 52 參考文獻 53

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