本文之主旨在探討安裝於彈性基礎上的流體輸送管的振動問題。樑是工程上最常見的機構元件，而流體輸送管之動態特性與一根承載流體的樑之振動現象相似，因此，本文利用Euler- Bernoulli樑理論，來推導流體輸送管的運動方程式，然後，探討流體輸送管之邊界支撐條件、彈性基礎之彈簧常數(或勁度係數)、管中流體之流速、以及流體流動所引起的科氏力(Coriolis force)等參數，對流體輸送管自由振動特性的影響。接著，則探討流體輸送管，承受分布外力作用時的強迫振動反應。
本文是利用有限元素法來進行流體輸送管的動態分析，因此，首要工作是推導流體輸送管的性質矩陣，為達此目標，本文先求流體輸送管元素的動能及位能，再將它們代入Lagrange 方程式而求得管元素的質量矩陣、阻尼矩陣及勁度矩陣，將上述各元素矩陣(element matrices)加以組合，則得對應於整個流體輸送管的總矩陣(overall matrices)。最後，本文以Jacobi法來求無科氏力效應之流體輸送管的自然頻率及振動模態，並以EISPAK軟體來進行有科氏力效應之自由振動分析；至於強迫振動方面，則以Newmark直接積分法來求流體輸送管，承受分布外力作用時的時間歷程圖與頻率-反應振幅曲線。

This purpose of this thesis is to study the vibration problem of the fluid-conveying pipes resting on the elastic Winkler foundations. Since the beam is one of the most popular structural members and the dynamic characteristic of a fluid-conveying pipe is similar to that of a beam carrying flowing fluid, this thesis derives the equation of motion of a fluid-conveying pipe by means of the Euler-Bernoulli beam theory. Next, the influences on the free-vibration characteristics of some parameters such as supporting conditions of the pipe, the stiffness of the elastic foundation, fluid velocity and Coriolis force due to flowing fluid are studied. Finally, the forced vibration responses of the fluid-conveying pipe due to distributed external forces are investigated.
In this thesis, the dynamic responses of the fluid-conveying pipes are performed by using the finite element method (FEM), thus, the essential work is to derive the property matrices of the fluid-conveying pipe. To this end, the kinetic energy and potential energy of a pipe element are determined first and then substituted into the Lagrange equation to obtain the mass matrix, damping matrix and stiffness matrix of the pipe element. The assembly of the latter element property matrices will determine the corresponding overall ones of the entire fluid-conveying pipe system. Finally, for the case of neglecting Coriolis force, the natural frequencies and the corresponding mode shapes are obtained by using the Jacobi method, and, for the case of considering Coriolis force, the free vibration analysis is conducted by using the software of EISPAK. As to the forced vibration analysis, the time histories and the frequency-response amplitude curves for any point on the fluid-conveying pipe are determined by using the Newmark’s direct integration method.

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