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研究生: 彭竑維
Peng, Hung-Wei
論文名稱: 開孔複合疊層曲面板受軸壓的最佳化自振分析
Maximization of Fundamental Frequencies of Axially Compressed Laminated Curved Panels with Hole against Fiber Orientations
指導教授: 胡宣德
Hu, Hsuan-Teh
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: 2010
畢業學年度: 98
語文別: 中文
論文頁數: 208
中文關鍵詞: 複合頻率軸向壓力開孔
外文關鍵詞: composite, frequency, axial, hole
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  • 由於複合材料具有高強度、高勁度、重量輕及低導熱之優越特性,已被廣泛應用於先進工業工程結構上。為避免外在環境之振動對結構物所產生的激振頻率與結構本身之自然頻率相近,而產生共振現象,造成結構甚大之變位與應力,超過使用材料之容許限度而破壞,因此結構物自然頻率的分析乃成為結構設計上之準則之一。
    本文利用有限元軟體ABAQUS來分析圓弧角、開孔大小,纖維角度、幾何形狀及軸向壓力大小,對複合疊層曲面板最高基本振動頻率所造成的影響,並應用費邦那西搜尋來求出複合疊層曲面板中,纖維之最佳排列角度及其對應之最高基本振動頻率。
    分析結果顯示,層板的最高基本振頻隨軸向壓力與長寬比的增加而減少,並且隨著開孔的擴大與圓弧角的增加而增加,故選擇適當的層板纖維角度與幾何形狀可提高其基本振頻,相信對未來複合層板廣泛使用之目的有所助益。

    Because of the composite laminated plates possess excellent characteristics such as high strength, high stiffness, lightweight, and low thermal conductivity, they have been widely used in advanced industrial engineering structures. To avoid structures producing resonance phenomenon and to make materials exceeding the limits allowed, structural analysis of natural frequency becomes the standard on structural design.
    In this thesis, ABAQUS finite element software is used to analyze the influence of arc angle, hole size, fiber orientations, geometric shapes and axial pressure on the maximum fundamental frequencies of composite laminated curved panel. The Fibonacci search is employed to find the optimal fiber orientations and its corresponding maximum fundamental frequency in the composite laminated curved panel.
    The results of the analyses show that the maximum fundamental frequency not only reduces with the increase of the axial pressure and the panel aspect ratio but also increases with the increase of hole size and arc angle. Therefore, choosing laminates fiber angle and suitable geometry can improve the fundamental frequency. So, it is useful in the design of composite curved panels in the future.

    中文摘要………………………………………………………………….i 英文摘要………………………………………………………………….ii 誌謝………………………………………………………………………iii 目錄………………………………………………………………………iv 表目錄…………………………………………………………………viii 圖目錄……………………………………………………………….........x 第一章 緒論…………………………………………………………….1 1.1 研究動機………………………………………………....1 1.2 研究方法………………………………………………....3 1.3 研究目的…………………………………………………4 1.4 內容與架構………………………………………………4 第二章 材料勁度矩陣..………………………………………………...6 2.1 殼元素簡介……………………………………………....6 2.2 材料主軸座標(1-2-3)系統下應力與應變關係……….....7 2.3 元素座標(x-y-z)系統下應力與應變關係…………….....9 2.4 合應力與合力矩關係……………………………….…..10 第三章 有限元素之振動分析..………………………………………14 3.1 振動方程式之推導………...……………………….......14 3.1.1 漢米爾頓原理(Hamilton’s principle)………...14 3.1.2 元素之振動方程式……………………………..15 3.1.3 結構之振動方程式……………………………..18 3.2 自然頻率與振態之分析………………………………...19 第四章 費邦那西搜尋………………………………………………...22 4.1 基本概念………………………………………………....23 4.2 基本定理………………………………………………...23 4.3 費邦那西數列…………………………………………....24 4.4 費邦那西搜尋……………………………………………24 4.5 數值分析流程……………………………………………25 第五章 ABAQUS程式與解析解比較及元素收斂性分析…………..26 5.1 異向性平板受平面初始外力時其振動頻率之解析解....26 5.2 ABAQUS程式與解析解比較...………………………....30 5.2.1 異向性平板受力驗證…………………………...30 5.2.2 複合層板自然振動頻率驗證……………...........30 5.2.3 複合疊層曲面板自然振動頻率驗證….………...31 5.3 元素收斂性分析……………………………………….....32 第六章 數值範例與比較討論…………...……………………….……34 6.1 問題敘述………………………………………….………34 6.2 固定複合疊層曲面板其直線長度與弧面長比值 (a/b)與圓弧角(φ),θopt與ωopt受軸向壓力與開 孔大小之影響…………………………..………......39 6.2.1 複合疊層曲面板其直線長度與弧面長比為一 (a/b=1) 圓弧角為5°(φ=5°) ……….………39 6.2.2 複合疊層曲面板其直線長度與弧面長比為一 (a/b=1) 圓弧角為60°(φ=60°)………..……40 6.2.3 複合疊層曲面板其直線長度與弧面長比為一 (a/b=1) 圓弧角為120°(φ=120°)…..…….42 6.2.4 複合疊層曲面板其直線長度與弧面長比為二 (a/b=2) 圓弧角為5°(φ=5°)………….……44 6.2.5 複合疊層曲面板其直線長度與弧面長比為二 (a/b=2) 圓弧角為60°(φ=60°)……………45 6.2.6 複合疊層曲面板其直線長度與弧面長比為二 (a/b=2) 圓弧角為120°(φ=120°)……...…47 6.2.7 複合疊層曲面板其直線長度與弧面長比為三 (a/b=3) 圓弧角為5°(φ=5°) …..…..…..…48 6.2.8 複合疊層曲面板其直線長度與弧面長比為三 (a/b=3) 圓弧角為60°(φ=60°)…….……...50 6.2.9 複合疊層曲面板其直線長度與弧面長比為三 (a/b=3) 圓弧角為120°(φ=120°)….……..51 6.3 固定複合疊層曲面板其開孔大小(d/b)與施加 軸力(N/Ncr),θopt與ωopt受長寬比(a/b)與圓 弧角(φ)之影響…………………………………..53 6.3.1 未開孔的複合疊層曲面板在未受軸力的 情形…..……........................................................53 6.3.2 未開孔的複合疊層曲面板所受軸力為 0.4Ncr………………………………………......54 6.3.3 未開孔的複合疊層曲面板所受軸力為 0.8Ncr………………………………………......55 6.3.4 開孔大小為d/b=0.4的複合疊層曲面板 未受軸力的情形………..…………….....…..56 6.3.5 開孔大小為d/b=0.4的複合疊層曲面板所 受軸力為0.4Ncr…………………..….....…..58 6.3.6 開孔大小為d/b=0.4的複合疊層曲面板所 受軸力為0.8Ncr…………………..…...…....59 6.3.7 開孔大小為d/b=0.8的複合疊層曲面板未 受軸力的情形………….………………....…..60 6.3.8 開孔大小為d/b=0.8的複合疊層曲面板所 受軸力為0.4Ncr…………………..…...…....61 6.3.9 開孔大小為d/b=0.8的複合疊層曲面板所 受軸力為0.8Ncr…………………..…...…....62 6.4 討論6-2與6-3節各個圖之間的相互關係……….63 第七章 結論與建議…………....………………………………………….66 7.1 結論…………………………………………………………66 7.1.1 複合疊層曲面板最高基本振頻率方面………..….66 7.1.2 複合疊層曲面板最佳化纖維角度方面…………...68 7.1.3 複合疊層曲面板模態圖…………………………...70 7.2 建議事項……………………………………………………70 參考文獻…………………………………………………………………….72 表 …………………………………………………………………………...78 圖 ………………………………………………………………………......91 附錄………………………………………………………………………...197 自述………………………………………………………………………...208

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