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研究生： 劉顏賓
Liu, Yen-Pin
論文名稱： 熱挫屈複合層板之顫振分析
Flutter Analysis of Thermally Buckled Composite Laminated Plates
指導教授： 蕭樂群
Shiau, Le-Chung
學位類別： 碩士
Master
系所名稱： 工學院 - 航空太空工程學系
Department of Aeronautics & Astronautics
論文出版年： 2005
畢業學年度： 93
語文別： 中文
論文頁數： 95
中文關鍵詞： 彎曲勁度 、熱挫屈 、熱挫屈後 、挫屈模態改變 、熱彎矩 、複合層板 、空氣動壓力 、超音速 、有限元素 、顫振
外文關鍵詞： bending stiffness, thermal buckling, thermal postbuckling, thermal moment, finite element, composite laminate, flutter, aerodynamic pressure, buckle pattern change, supersonic
相關次數： 點閱：139  下載：3 
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    • 　　本文採用von Karman幾何大變形假設，推導一54個自由度的高階三角形板元素，用以分析及討論複合層板在承受溫度場改變下之熱挫屈後的顫振行為。當溫度高於臨界挫屈溫度時，複合層板進入熱應力後挫屈階段，挫屈後層板之總位移可視為靜態變形與動態變形的總合。線性顫振分析須於頻率域中求解，通常臨界動壓力值出現在層板之第一(1,1)與第二(2,1)模態重合時，但複合層板因纖維排列方向及層板長寬比特性之影響，使得臨界動壓力會在不同情況下由不同模態之合併而產生。一般而言，顫振邊界的高低與層板的整體勁度有關，尤其是在超音速氣流方向的彎曲勁度更左右著 大小，當溫度逐漸升高至挫屈溫度時，能量發生不穩定現象，平面壓應力的產生造成層板的勁度降低，因此挫屈時之顫振邊界會比未挫屈前來得低，而當層板發生挫屈之後，因挫屈變形所引起的平面張力會增加層板的彎曲勁度，所以當溫度漸漸升高時，張力將會使彎曲勁度提升。對於角交複合層板而言，在氣流方向上的彎曲勁度以θ＝0°時為最大，隨著纖維排列的改變，其彎曲勁度亦隨之降低。因此，此種層板的顫振邊界與其纖維角度的排列有著密切的關係。層板在後挫屈範圍內發生的挫屈模態改變(Buckle pattern change)現象，可以提供額外的勁度，造成顫振邊界上升。當層板在厚度方向受到不均勻的溫度梯度時，會使得層板產生熱彎矩，造成側向變形，進而產生平面張應力且增加層板之彎曲勁度，當溫度由室溫開始上升，層板的靜態變形型態將不再是平坦運動，會使得平坦與挫屈區域間的穩定邊界消失，並且明顯穩定複合層板的動態行為且提升顫振邊界。在非線性分析方面，若將λ固定而溫度開始增加時，層板的最大位移也開始增加，另外，最大的層板速度也將會隨溫度而增加。另一方面，當溫度固定而 增加時，則最大層板位移隨著空氣動壓力之增加將不會有太大的變化，但板的最大振動速度將會隨空氣動壓力而增加。

    　　Base on the von Karman large deflection assumptions, a 54 degree-of-freedom high precision high order triangular plate element is develop for flutter analysis of a thermally buckled composite laminated plate. For a buckled plate, the total response of the plate is considered to be the sum of the displacement of the buckled static deformation and that due to small dynamic oscillation about the static deformed shape. The flutter boundaries obtained in the linear flutter analysis, linear flutter analysis is solved in frequency domain. In general, the flutter coalescence pair is between the flutter modes (1,1) and (2,1). However, due to the special characters of the composite laminates, the coalescence pair may be between higher modes.Usually, the stiffness of the plate is the main factor in determining the flutter boundary, especially in the direction of supersonic airflow. But for a thermally buckled plate, the in-plane tensile force will increase the bending stiffness of the plate which in turn gives higher flutter boundary.The maximum value of flutter boundary for an angle-ply laminate is occurred when the fiber is orientated in the direction of the supersonic airflow, i.e. the x-direction. The buckle pattern change phenomenon occurred in the post-buckling range will raise the flutter boundary of the plate due to the stiffness of the plate altered by the phenomenon. Temperature gradient through the plate thickness will initially bend the plate that makes the stability boundary between the flat and buckled regions disappear. Temperature gradient will also increase the overall stiffness of the plate, stabilize the laminate plate, and give higher flutter boundary.For nonlinear flutter analysis, when λ is fixed, the maximum plate displacement and its velocity will increase with temperature. On the other hand, if the temperature remains constant, the maximum plate displacement will not vary much with the increase of the aerodynamic pressure. But the maximum plate vibrating speed will increase with aerodynamic pressure.

    目 錄 中文摘要 英文摘要 誌 謝 目錄............................................................................I 表目錄........................................................................III 圖目錄.........................................................................IV 符號說明.....................................................................VIII 第一章 緒論....................................................................1 第二章 公式推導...............................................................10 2.1複合層板基本公式............................................................10 2.2應變能、動能與功能..........................................................13 2.3有限元素推導................................................................14 2.4 動態平衡方程式.............................................................20 2.5求解流程....................................................................21 2.5.1 線性顫振之頻率域公式...........................................22 2.5.2非線性顫振之時域模態公式........................................23 第三章 結果與討論.............................................................28 3.1線性顫振分析................................................................30 3.1.1 Cross-ply正交對稱複合層板................................................30 3.1.2 Angle-ply角交對稱複合層板................................................34 3.2非線性顫振分析......................................................38 3.2.1 Cross-ply正交對稱複合層板......................................38 3.2.2 Angle-ply角交對稱複合層板......................................40 第四章 結論..................................................................44 參考文獻.......................................................................47 附錄...........................................................................53 附表...........................................................................55 附圖...........................................................................57

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