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。本模型把管壁視為等向性圓柱厚殼，並將管內流體視為層流，且為不可壓縮的黏滯流體。由傳統彈性理論來描述管壁運動，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%，因此再討論此三組模態，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。

A mathematical model closer to the artery is proposed to describe the pressure wave propagating in the artery. We treat the wall as an isotropic and thick walled cylindrical shell and the fluid as an incompressible and laminar. The motion of the wall is described by the classical elasticity theory 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. Then, we could realize the property of these modes further by the different parameters.

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