渦漩引致振動為一實際之工程問題，例如航太工程中的機翼飛行時之振動。當一結構物在流場
中與流體交互中用時，流體作用於結構物上的作用力會造成結構的振動，更進一步當此所鎖相
放大的情形發生時更可能造成結構物的毀損。因此本研究嘗試建立一沉浸邊界法來模擬一圓柱
體在一均勻流場中所產生的渦漩引致振動現象。在所建立的數值模式中，此一圓柱受力後可在
流動平行方向與垂直方向運動。在本研究中主要探討入流速度的變化對渦漩引致振動的效應，
所預測之圓柱所受之氣動力係數在時域與頻域中呈現。在鎖相放大的遲滯驟升取線區可發現圓
柱的升阻力係數的極大值，而此時之振動頻率與圓柱自然頻率之比是處於接近一之軟性鎖相放
大。此外，一般稱為2S的渦漩逸放現象可在圓柱處於低頻振動時被發現，而當振動振幅變大時
可觀察到被稱為C(2S)模態。本數值模式經與他人之數值與實驗結果相比有良好之一致性，故本
數值模式可用來做研究渦漩引致振動之有效工具

Vortex-induced vibration (VIV) of structures is one of the practical interests in various engineering studies such as wind engineering, ocean engineering, aerospace engineering, and so on. When a structure is exposed to a flow field, the resultant hydrodynamic force may cause the vibrations of the structures. Furthermore, this vibration phenomenon may cause the failure of the structure especially for the so-called lock-in situation. In this present study, VIV of a circular cylinder placed in a uniform fluid flow at moderate Reynolds number is simulated using the direct-forcing immersed boundary method. The cylinder is allowed to vibrate in transverse direction and both in the in-line and transverse directions. The effect of reduced velocity on VIV is discussed in this study. Aerodynamic coefficients of a freely vibrating cylinder are analyzed in time and spectral domains. The maximums of the lift coefficient and the mean drag coefficient show hysteresis jumps at low end of the lock-in region. Hysteresis in the response of the cylinder is observed at the low end of the synchronization region. The ratio between the vortex shedding frequency and the natural frequency of the structure experiences the so-called soft lock-in. Moreover, the 2S vortex shedding mode can be found at low amplitudes of vibrations of the cylinder. The C(2S) mode is observed when the oscillation amplitude is large. Good agreements of the results with the previous experimental and numerical data prove the capability of the present method. This established model can be useful for the investigation of VIV of the structures.

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