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研究生:陳宏吉
研究生(外文):Chen, Hong-Ji
論文名稱:氣浮彈力系統之分岔與動態行為分析
論文名稱(外文):Bifurcation And Dynamic Behavior Analysis Of Aeroelastic System
指導教授:汪正祺
指導教授(外文):Wang, Cheng-Chi
口試委員:王啟昌郭昭霖林大偉汪正祺
口試委員(外文):Wang, Chi-ChangKuo, Chao-LinLin, Da-WeiWang, Cheng-Chi
口試日期:2012-07-26
學位類別:碩士
校院名稱:遠東科技大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:81
中文關鍵詞:氣浮彈力系統微分轉換法分岔圖
外文關鍵詞:AeroelasticDifferential transformation methodBifurcation diagram
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氣浮彈力系統是融合結構、慣性力及空氣動力等理論所產生的複雜系統,且彼此間會有交互作用,有時會造成飛行器不穩定、振顫等現象。然而,此振顫現象若長時間發生,將會導致飛行器之機翼結構產生破損,進而造成許多飛機失事等悲劇發生。因此為避免類似情形產生,本文將針對在低頻及次音速飛行時的系統參數,模擬機翼所產生的所有動態行為。同時為有效避免數值誤差,本文將以微分轉換法針對氣浮彈力系統探討在特定參數之下的非線性動態性能,並以分岔圖、軌跡圖、截面圖、頻譜圖及李奧維指數來判斷系統所存在的狀態是否為非週期現象。
當初始值α=1~10、h=0.02、γ=46時,其非線性區域都在-4.292≦β≦-4.045,其中在-4.292≦β≦-4.29為混沌,其餘的都是準週期。當初始值α=10、h=0.005~0.02、γ=45 時,其非線性區域都在-4.202≦β≦-3.954,其中在-3.96≦β≦-3.954、-4.2≦β<-4.199、-4.202≦β<-4.201為混沌,其餘的都是準週期。
由上述結果可知氣浮彈力系統在特定的參數條件下具有非線性動態性能,為有效預估與控制非線性狀態,我們可以由頻譜圖及李奧維指數來判斷系統是否為週期現象、準週期現象與混沌現象的分岔點。並做為後續設計氣浮彈力系統的參考。

An aeroelastic system combines several complex theories of physics. These principles will cause instability situations or be interacted each other. If this behavior occurs, it will result in the fatigue problems or structural damages on the wings of aircrafts. In order to avoid these conditions to occur, this paper studies the nonlinear dynamic motions of aeroelastic system under specific operating conditions and employs differential transformation method (DTM) to decrease the calculation errors. Also, the bifurcation diagram, Poincare map, and power spectra are used to analyze the numerical results. The results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and non-periodic responses of the system.
When the initial values are assumed as α=1~10,h=0.02,γ=46, the non-periodic region occurs over the interval of -4.292≦β≦-4.045 with chaotic motion at -4.292≦β≦-4.29, and the other intervals are quasi-periodic behaviors. When the initial values are assumed as α=10,h=0.005~0.02,γ=45, the non-periodic region occurs over the interval of -4.202≦β≦-3.954, with chaotic motion at -3.96≦β≦-3.954, -4.2≦β<-4.199, -4.202≦β<-4.201, and the rest are quasi-periodic.
In order to estimate and control the chaotic state effectively, the maximum Lyapunov exponents are used to verify whether the system ouccurs chaos phenomena and as a follow-up design of reference for aeroelastic system.

中文摘要 I
英文摘要 II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號 X
第一章 序論 1
1-1 前言 1
1-2 文獻回顧 1
1-3 本文架構 2
第二章 氣浮彈力系統之數學模型 3
2-1 運動方程式 3
2-2 數值模擬 5
第三章 分析方法 9
3-1分岔圖 9
3-2相空間軌跡法 10
3-3龐卡萊截面法( Poincaré maps) 10
3-4頻譜分析及李奧維指數 12
第四章 數值模擬結果與討論 13
4-1 翼後緣與機翼所夾之角度(β)對系統的影響 13
4-1-1 俯仰角初始值的變化與β對系統的交互影響 13
4-1-1-1 軌跡相平面圖 13
4-1-1-2 頻譜分析 13
4-1-1-3 分岔圖與截面圖 14
4-1-1-4 李奧維指數 14
4-1-1-5 不同俯仰角初始值的變化 14
4-1-2 振幅初始值的變化與β對系統的交互影響 27
4-1-2-1 軌跡相平面圖 27
4-1-2-2 頻譜分析 27
4-1-2-3 分岔圖與截面圖 27
4-1-2-4 李奧維指數 28
4-1-2-5 不同振幅初始值的變化 28
4-2 翼前緣切線與機翼所夾之角度(γ)對系統的影響 38
4-2-1 俯仰角初始值的變化與γ對系統的交互影響 38
4-2-1-1 軌跡相平面圖 38
4-2-1-2 頻譜分析 38
4-2-1-3 分岔圖與截面圖 39
4-2-1-4 李奧維指數 39
4-2-1-5 不同俯仰角初始值的變化 39
4-2-2 振幅初始值的變化與γ對系統的交互影響 52
4-2-2-1 軌跡相平面圖 52
4-2-2-2 頻譜分析 52
4-2-2-3 分岔圖與截面圖 53
4-2-2-4 李奧維指數 53
4-2-2-5 不同振幅初始值的變化 54
4-3 β與γ對系統的交互影響 66
4-3-1 γ=50~-50時,不同β對系統的影響 66
4-3-2 β=18~-18時,不同γ對系統的影響 66
第五章 結論與未來研究方向 75
5-1 結論 75
5-2 未來研究方向 79
參考文獻 80

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