臺灣博碩士論文加值系統

本文提出一個更為接近動脈血管的數學模型，描述壓力波在血管中的傳遞模態。本模型把彈性管管壁視為圓柱厚殼，並將管內流體視為層流，且為不可壓縮的黏滯流體。由肌肉彈性假設為彈簧來描述管壁運動，也加入了管壁具有黏滯性的條件，而且配合流體的線動量方程以及連續條件，推導出統御方程式。由於本文是考慮波動行為，因此求解過程中，將代入波的諧和條件，最終可由特徵方程式得到三組有意義的特徵值－波數(wave number)。本文將個別討論此三組特徵值，來說明三組壓力波的傳遞模態，其中包括波速，以及波的衰減；由於在動脈的能量分布中，由管壁振動的彈性位能佔了98%，遠超過血液本身流動的2%，再加上管的彈性模數和管壁的黏滯性再來討論此三組模態，個別在彈性管的能量分布。然而藉著不同參數的影響來更加了解這些模態的特性。之後再利用ADINA分析軟體與理論作比較。

A mathematical model closer to the artery is proposed to describe the pressure wave propagating in the artery. We treat the wall as a elastic wall and thick walled cylindrical shell and the fluid as an incompressible and laminar. The muscle is simulated by elastic foundation and put into the wall of managing having a viscid condition and the motion of fluid by the linear momentum equation and the continuity equation, and therefore, the governing equations are derived. We consider the propagation of harmonic waves in the governing equations. In that way, we can get three significant eigenvalues(wave number). The thesis discusses three eigenvalues individually and explains the pressure wave propagation of three modes, includes wave speed, wave decay and energy distribution. Since the elastic potential energy occupies more than 98% of mechanical energy in the arteries, which is larger than 2% of kinetic energy of flowing blood. Else join elastic wall and wall of managing having a viscid condition to analysis .Then, we could realize the property of these modes further by the different parameters. .Then, we utilize analysis of software (ADINA) and theory to compare.

摘要................................................................................................IV
ABSTRACT....................................................................................V
誌謝................................................................................................VI
目錄..............................................................................................VIII
表目錄..............................................................................................X
圖目錄..............................................................................................X
符號說明......................................................................................XIII
第一章 緒論.....................................................................................1
1.1 前言.....................................................................................................1
1.2 文獻回顧.............................................................................................2
1.3 研究動機與目的.................................................................................5
1.4 論文架構.............................................................................................7
第二章 物理模型架構.....................................................................8
2.1彈性管壁的統御方程式推導..............................................................8
2.1.1應變－位移關係式...................................................................9
2.1.2管壁為黏滯性的應力－應變關係式....................................11
2.1.3平衡方程式.............................................................................13
2.1.4模擬肌肉包覆血管的自由振動.............................................15
2.2管內流體的統御方程式推導...........................................................17
2.2.1線動量守恆.............................................................................17
2.2.2連續方程式.............................................................................20
2.3 總結...................................................................................................21
第三章 解法.....................................................................................23
3.1統御方程式的簡化............................................................................23
3.2流體未流動之下的壓力波................................................................26
3.3流體未流動之下的能量分布...........................................................36
第四章 數值分析與比較...............................................................44
第五章 結論與建議.......................................................................61
5.1結論....................................................................................................61
5.2建議....................................................................................................63
參考文獻.........................................................................................64
自述.................................................................................................67

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