動脈血管循環很早就有理論的發展，不過大都偏重在流體的行為研究，或者是為了實驗方便而過度簡化模型。本文提出一個新的數學模型，描述壓力波在充滿黏性不可壓縮流體的等向性彈性管中的傳輸行為。本模型考慮管徑變化對流體造成的影響，以及管內預壓對壓力波的影響，而且同時考慮徑向和軸向的振動。我們把管壁視為圓柱薄殼，而且管內流體滿足線動量方程以及連續條件之下，推導出統御方程式。於求解過程中，將變數-壓力、最大流速分解成平均項和擾動項，線性化統御方程式，最後從特徵方程式得到壓力波的色散關係 ( dispersion relation)，以及衰減因子--波數(wave number)的虛部項。本文將討論不同參數相對於波速，以及波能量衰減的影響，藉此更加了解壓力波的特性。

　The theory for circulation of arteries has been developed early, but most studies are emphasized on fluid behavior or some models for experimental utility are too simplified. A new mathematical model is proposed to describe the pressure wave propagating in the isotropic elastic tube filled with viscous and incompressible fluid. In this model, the effects caused by variation of tube diameter on fluid and the normal stress due to pre-pressure on tube wall are all took into account. The radial and longitudinal vibrations both are introduced. We treat the tub wall as a thin walled cylindrical sell also fluid coincides the linear momentum equation and continuity equation, and therefore, the governing equations are derived. To linearize the governing equation, variables, pressure and maximum fluid velocity are separated into average term and disturbed term. In that way, the dispersion relation of pressure waves is obtained from the characteristic equation. The thesis also discuss the effect of different variables on wave velocity and on energy decay, so that we can realized the property of pressure wave more.

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