這篇論文研究主題是傾斜流體之渦流引致圓柱振動之研究，流體及振動圓柱之間的交互作用及其影響通常是主要探討及研究的課題，我們利用有限差分法來獲得圓柱受力情況，然後再結合Runge-Kutta 四階公式求解動態方程式來獲得下一個time step的圓柱位置及其物理量，重複上述程序我們將可得到圓柱隨著時間的反應。大部分的研究聚焦在尖峰振幅及其大小，其發生的原因在於系統振動頻率接近或剛好位於均勻流通過固定圓柱時其自然振動頻率的位置上。在VIV的模擬上，除了第一共振，我們還發現第二共振的現象。第二共振的現象可能是由於系統振動頻率的2倍接近或剛好位於均勻流通過固定圓柱時之渦流擺盪頻率上。系統的振動頻率是ㄧ個很重要的參數，經常被拿來研究或探討它的影響及重要性，而且它的值也代表圓柱垂直應力（或垂直位移）的振動頻率。相反地，圓柱之軸向應力（或軸向位移）的振動頻率較少被討論或進ㄧ步研究。在我們的研究中，我們將探討圓柱軸向應力的振動頻率及其大小對於第一共振及第二共振的影響。
為驗證本研究數值模式之正確性，本研究模擬分析一均勻流場分別通過一固定圓柱、一水平振動圓柱、一垂直振動圓柱、一旋轉振動圓柱等4種類型的情況，藉由數值模擬分析的成果與其他研究成果（包括實驗成果、數值模擬成果等）相互對照及比對，比對結果顯示，對於圓柱受力情況、圓柱後方漩渦的尺寸、漩渦剝離擺盪的情況及頻率、流線流場的模式等成果皆具有相當高的精確性。本研究進一步探討均勻流場通過一強迫振動圓柱，圓柱振動方向與均勻流場有一傾斜角度，在給定不同的振動頻率、不同的傾斜角度時、對於通過圓柱時圓柱受力及後方漩渦擺盪模式進一步探討及研究，並對於Morison方程式的應用及限制進一步分析比對，嘗試藉由不同的模擬案例將公式使用上的限制給予標示出來。

Vortex induced vibration of a circular cylinder in an inclined flow is a major subject in this thesis, the interaction and effect between a moving cylinder and fluid is always focused and investigated. We used a finite differences method to get the forces on cylinder, and then combined a Runge-Kutta four order approximate method to get a new position of a cylinder at next time step, repeated above procedure and we will get the solutions of a time series of cylinder response for VIV simulations. Most of papers focus on the peak amplitude and its scale due to the shedding frequency of system is near or at the fs, where fs is the shedding frequency of a uniform flow past a stationary cylinder. Except the “first resonance”, we found the “second resonance” in the VIV simulations. The “second resonance” occurs due to the natural shedding frequency of system is near or at the twice of the reduced frequency of the oscillator “fs=2F1”. The natural shedding frequency of a body is a key parameter, it always be discussed its effect and importance, and its value is also presented the frequency of lift force (or displacement on Y direction) of a body. On the contrary, the frequency of in-line force (or displacement on X direction) and its effect is seldom be investigated and discussed. In this study, we will discuss the effect of frequency of in-line force and the scale of “first resonance” and “second resonance” for VIV simulations.
In order to verify the accuracy of our numerical model, this study simulated four different types for the cases of uniform flow past a circular cylinder with stationary, streamwise, transversal and rotational oscillating, respectively. The simulation results are compared with the study results of other paper by experimental and numerical methods, and the comparison show good agreement and high accuracy in the range of the in-line and lift forces on the cylinder, the main wake size behind the cylinder, the vortex shedding mode and the streamline pattern of the flow field. Furthermore, this study investigates a uniform flow past an inclined oscillating cylinder which is forcing oscillation in a range of 00 ~ 900 for the inclined angle (with respect to the X-direction of the Cartesian coordinates system). The effects of giving the different forced frequencies of a cylinder were investigated and discussed. And the application and restriction of Morison’s equation will also be studied and investigated in different input conditions.

Chinese Abstract Ⅰ
English Abstract Ⅲ
Contents Ⅴ
Notation Ⅸ
Figure caption F-1
List of table F-14
Chapter 1. Introduction 1-1
Chapter 2. Literature review 2-1
Chapter 3. Numerical method 3-1
3.1 Governing equations 3-1
3.2 Coordinate transformation and boundary condition 3-1
3.3 Grid type and computation procedure 3-4
3.4 Runge-Kutta method 3-6
3.5 Non-dimensional group 3-7
Chapter 4. Numerical validations 4-1
4.1 Convergence study. 4-1
4.2 Uniform flow past a fixed circular cylinder, Re=40 and 550. 4-5
4.3 Uniform flow past a fixed circular cylinder, Re=3,000 4-7
4.4 A harmonic oscillating circular cylinder in static fluid, Re=100, KC=5 4-9
4.5 Uniform flow past a transversal oscillating circular cylinder,
Re=500, Ymax/D = 0.25, frequency ratio F = f/fs =0.89 4-10
4.6 Uniform flow past a circular cylinder with rotational oscillati0n,
Re=500, forcing Strouhal number S=π/6 4-11
4.7 Oscillating flow past a circular cylinder with spring supported and
restricted vibration along the streamwise direction only, Re=200, KC=4 4-13
4.8 Uniform flow past a circular cylinder with spring supported and restricted
vibration along cross-flow direction only, Re=2,000~11,840, U*=2~12 4-14
4.9 Uniform flow past a circular cylinder with two springs supported
in the laminar flow regime (60＜Re＜170). 4-15
Chapter 5. An arbitrary oscillating cylinder in uniform flow 5-1
5.1 Uniform viscous flow across a translating circular cylinder, Re=3,000. 5-3
5.1.1 Streamline patterns development（βA = 1, ε = 1, Re = 3,000） 5-4
5.1.2 The separation points（β A= 1, ε = 1, Re = 3,000） 5-6
5.1.3 The results for ε= 1 with various βA values 5-7
5.1.4 The forces on cylinder 5-8
5.1.5 The remark 5-10
5.2 Uniform viscous flow past a simultaneous stream-wise and transversal
moving circular cylinder (Re = 100, KC=5, inclined θ= 00 and 450) 5-11
5.2.1 Uniform flow past a cylinder with streamwise oscillation
(Re = 100, KC=5, inclined θ=00, F=0.8 ~ 1.22) 5-12
5.2.2 Uniform flow past an oscillating cylinder in the direction of an
inclined 45 degrees (Re = 100, KC=5, inclined θ=450, F=0.8 ~ 1.22) 5-16
5.3 Uniform flow past an oscillating cylinder in the direction of 7 different
inclined angles (Re=100, KC=5, F=1.2159, inclined angle θ= 50, 100,
300, 450, 600, 750 and 900) 5-20
5.3.1 Uniform flow past an oscillating cylinder in the direction of an
inclined 5 degrees (Re=100, KC=5, inclined angle=50) 5-21
5.3.2 Uniform flow past an oscillating cylinder in the direction of an
inclined 10 degrees (Re=100, KC=5, inclined angle=100) 5-23
5.3.3 Uniform flow past an oscillating cylinder in the direction of an
inclined 30 degrees (Re=100, KC=5, inclined angle=300) 5-26
5.3.4 Uniform flow past an oscillating cylinder in the direction of an
inclined 45 degrees (Re=100, KC=5, inclined angle=450) 5-28
5.3.5 Uniform flow past an oscillating cylinder in the direction of an
inclined 60 degrees (Re=100, KC=5, inclined angle=600) 5-29
5.3.6 Uniform flow past an oscillating cylinder in the direction of an
inclined 75 degrees (Re=100, KC=5, inclined angle=750) 5-30
5.3.7 Uniform flow past an oscillating cylinder in the direction of an
inclined 90 degrees (Re=100, KC=5, inclined angle=900) 5-31
5.3.8 The summary of a uniform flow past an oscillating cylinder in
the direction of 7 different angles (Re=100, KC=5, F=1.2159,
inclined angle=50, 100, 300, 450, 600, 750 and 900) 5-33
5.4 Uniform flow past an oscillating cylinder with an inclined angle
30 degrees at fixed Stoke number (β=35, KC=3 ~ 9, Re=105 ~ 315,
F=0.875 and 0.975) 5-37
5.4.1 Uniform flow past an oscillating cylinder with an inclined angle
30 degrees for [Re, KC, F]=[105, 3, 0.875], [105, 3, 0.975],
[140, 4, 0.875] and [140, 4, 0.975]. 5-38
5.4.2 Uniform flow past an oscillating cylinder with an inclined angle
30 degrees for [Re, KC, F]=[175, 5, 0.875] and [175, 5, 0.975] 5-41
5.4.3 Uniform flow past an oscillating cylinder with an inclined angle
30 degrees for [Re, KC, F]=[210, 6, 0.875], [210, 6, 0.975],
[280, 8, 0.875] and [280, 8, 0.975]. 5-42
5.4.4 Uniform flow past an oscillating cylinder with an inclined angle
30 degrees for [Re, KC, F]=[315, 9, 0.875] and [315, 9, 0.975]. 5-45
5.4.5 The summary of a uniform flow past an oscillating cylinder
in the direction of an inclined angle 30 degrees for 12 different
combinations of Re number, KC number and frequency ratio. 5-46
Chapter 6. Vortex induced vibrations of two degrees of freedom 6-1
6.1 Vortex induced vibration of a cylinder in the inclined flow at α = 300 6-3
6.2 Vortex induced vibration of a cylinder in the inclined flow at α = 450 6-23
6.3 Vortex induced vibration of a cylinder in the inclined flow at α = 600 6-28
6.4 Vortex induced vibration of a cylinder in the inclined flow at α = 750 6-29
VIII
6.5 Vortex induced vibration of a cylinder in the inclined flow at α = 900 6-31
6.6 The “second resonance” branch of VIV problem. 6-33
6.7 The effect of the inclined flow on the cylinder response 6-37
6.8 Vortex induced vibration of a cylinder in the inclined flow at the same
Reynolds number 100 for the range of the reduced velocity
U*=1~14 6-45
Chapter 7. Conclusions 7-1
References Reference-1
Appendix-A Appendix-A-1
Appendix-B Appendix-B-1
Appendix-C Appendix-C-1
Appendix-D Appendix-D-1
Appendix-E Appendix-E-1
Appendix-F Appendix-F-1
Appendix-G Appendix-G-1
Appendix-H Appendix-H-1
Appendix-I Appendix-I-1
Appendix-J Appendix-J-1
Appendix-K Appendix-K-1

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