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研究生:高震宇
研究生(外文):Chen-Yu Kao
論文名稱:磁流變流體之介觀理論分析
論文名稱(外文):Research on the Mesoscopic Theory of Magnetorheological Fluids
指導教授:陳國慶陳國慶引用關係
學位類別:碩士
校院名稱:國立暨南國際大學
系所名稱:土木工程學系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:55
中文關鍵詞:介觀觀念磁流變流體混體理論內變數分布函數
外文關鍵詞:mesoscopic conceptmagnetorheological fluidsmixture theoryinternal variabledistribution function
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介觀(mesoscopic)的觀念最初發展源自探討液晶(liquid crystals)材料的理論。本文是以連體力學為基礎,採用了混體(mixture)的概念以及介觀理論,引進介觀變數(mesoscopic variable)來描述磁流變材料內部磁性顆粒分子的排列。介觀理論的想法是擴展場變數的空間域,將原本的位形空間(configuration space)擴增至介觀空間(mesoscopic space),此介觀空間包含了新引進的介觀變數。
接著考慮電磁場的作用下,推導介觀與宏觀的電磁場守恆律以及力學平衡方程式,並且適當地建構介於宏觀量與介觀量之間的關係式。藉由多極矩展開(multipole moment expansion)的觀念,可得到宏觀內變數(internal variable)對時間的演化(evolution)方程式。最後,針對介觀速度函數之特殊組成形式提出兩個可能的假設情形,並對介觀分布函數(mesoscopic distribution function)之二極矩對時間的演化方程式做一探討。
The mesoscopic concept, which was originally developed in the theory of liquid crystals, is introduced for the description of magnetorheological (MR) materials. This mesoscopic theory is constructed based on the mixture concept of continuum mechanics. The idea of the mesoscopic theory is that the configuration space is augmented to the mesoscopic space which includes the newly-introduced mesoscopic variable characterizing the arrangement of the particles.
On account of the contribution of magnetic field, the mesoscopic and macroscopic balance equations are formulated and the relationship between the mesoscopic and macroscopic quantities are established. By the concept of multipole expansion we derive the mesoscopic-based macroscopic evolution equations of the internal variables. In virtue of simple constitutive equations for the velocity of the mesoscopic variable, two equations for the second moment of the distribution function are also given.
誌 謝 …………………………………………………………………………………i
中文摘要 ………………………………………………………………………………...ii
Abstract ………………………………………………………………………………...iii
目 錄 ………………………………………………………………………………..iv
第一章 導論 …………………………………………………………………………..1
1.1 文獻回顧 …..…………………………………………………………………...2
1.2 研究目的 …..…………………………………………………………………...4
1.3 本文架構 …..…………………………………………………………………...5
第二章 介觀守恆律 …………………………………………………………………6
2.1 介觀理論簡介—以液晶材料為例 …………………………………………….6
2.1.1 物質的特別相—液晶相 …………………………………………………6
2.1.2 液晶材料現象學理論的發展沿革 ……………………………………….8
2.2 介觀觀念 ……………………………………………………………………...11
2.2.1 內部結構有序度的描述 ………………………………………………..11
2.2.2 磁流變材料獨特的相轉換 ……………………………………………..11
2.2.3 介觀空間 ………………………………………………………………13
2.2.4 介觀分布函數 ………………………………………………………….14
2.3 電磁學方程式 ………………………………………………………………...15
2.4 力學平衡方程式 ……………………………………………………………...17
第三章 宏觀守恆律 ………………………………………………………………..23
3.1 微觀世界和宏觀世界脫節之處的探討 ……………………………………...23
3.2 電磁學方程式 ………………………………………………………………...23
3.3 力學平衡方程式 ……………………………………………………………...24
3.4 熵不等式的探討 ……………………………………………………………...28
第四章 內變數的演化方程式 ………………………………………….………..31
4.1 宏觀內變數的廣義演化方程式 ……………………………………………...31
4.2 介觀分布函數二極矩的演化方程式 ………………………………………...33
第五章 總結 …………………………………………………………………………38
5.1 結論 …………………………………………………………………………...38
5.2 未來研究方向 ………………………………………………………………...40
參考文獻 ……………………………………………………………………………….41
附錄 ……………………………………………………………………………………..48
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