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研究生:李威慶
研究生(外文):Wei-Cing Li
論文名稱:偶合杜飛系統之複雜分歧現象
論文名稱(外文):The complex bifurcations of a coupled Duffing system
指導教授:蕭永嘉蕭永嘉引用關係
指導教授(外文):Yung-Chia Hsiao
學位類別:碩士
校院名稱:明道大學
系所名稱:材料科學與工程學系碩士班
學門:工程學門
學類:材料工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:20
中文關鍵詞:共維度二第二響應主要響應
外文關鍵詞:secondary responseprimary responsecodimension-two
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杜飛方程式 (Duffing equation) 為常見的非線性微分方程式,具有週期外
力與三次方非線性項。早期文獻中發現到第二響應的次簡諧解會與主要響應的
次簡諧解同時存在。Hsiao 和 Tung 發現偶合的杜飛方程式其第二響應會從主
要響應分離。本論文發現新的第二響應與主要響應分離現象。當週期外力振幅
變大,週期解的兩個週期加倍分歧點彼此相互接近,然後合併在一起消失。在
週期加倍分歧點合併消失的同時,原本屬於主要響應的次簡諧解會忽然分離出
來變成第二響應,並與主要響應的週期解共存。此現象與先前研究中第二響應
由主要響應的次簡諧解分離出來不同,為新的主要響應與第二響應分離現象。
論文中應用發射法求得系統之週期解和次簡諧解,而頻率響應圖則是以簡諧平
衡法求之,其穩定性分析則是利用 Floquet 理論求得。
Duffing equation is one of the common nonlinear differential equations with a harmonic driving force and cubic nonlinearity. Many investigations described that the secondary responses coexist with the primary responses. Hsiao and Tung observed that the subharmonic orbits of the secondary responses separate from the subharmonic orbits of the primary responses via the coalescence of two saddle-node bifurcations points of the subhramonic orbits in a couple Duffing system. This thesis observed another separation of the secondary responses and the primary responses. The subharmonic orbits of the secondary responses separate from the primary responses via the coalescence of two period doubling bifurcations points of the periodic orbits. To analyze the phenomenon, the periodic orbits and the subharmonic orbits are detected by using the shooting method and the frequency responses are obtained through the harmonic balance method. Besides, the stability of the obtained orbits is performed using the Floquet theory.
摘要……………………………………………IV
Abstract ………………………………………V
第一章 序論……………………………………1
第二章 方程式的週期解………………………4
第三章 週期解和次簡諧解的穩定性分析……7
第四章 新式主要響應與第二響應分離現象…9
第五章 結論 …………………………………17
參考文獻………………………………………18
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