本研究針對具繫纜之浮式結構與波浪互相作用的問題進行解析，分別為(1)波浪與自由浮式結構物互相作用的問題、(2)波浪與彈簧錨碇浮式結構物互相作用的問題以及(3)波浪與纜繩錨碇浮式結構物互相作用的問題。對波浪與自由浮式結構物互相作用的問題，考慮波浪、浮式結構物於頻率領域之完整互相作用問題，結構的運動、波浪場包含衝動(surge)、浮動(heave)以及翻轉(pitch)等三個運動自由度，以Sarpakaya and Isaacson (1981)的求解概念將問題分解為散射問題與三個方向的單位振幅結構物運動之輻射問題，最後利用結構物運動方程式合併求解整個問題。理論求解散射問題以及結構物水平方向運動和垂直方向運動之輻射問題，在文獻中已有完整敘述，本研究主要為提出單位振幅結構物轉動之輻射問題的理論解析解，然後合併散射問題與三個自由度的輻射問題來描述結構物運動，利用本研究的解析解計算浮式結構物之運動，與波浪的反射係數，與Ijima (1972)的數值計算結果比較，顯示很好的一致性。對波浪與彈簧錨碇浮式結構物互相作用的問題，文中考慮波浪、浮式結構物、受波浪流阻力的彈簧於頻率領域之完整互相作用問題，結構的運動、波浪場與作用於彈簧的Morison波力均包含三個運動自由度，而Morison波力為一非性線項，本研究以Lorentz’s hypothesis of equivalent work來將此項線性化，將彈簧的Morison波力與繫留力以及作用於浮式結構物的波力利用結構物運動方程式合併求解整個問題，本研究的解析解計算纜繩無阻力作用的波浪反射係數與Ijima (1972)的計算結果顯示很好的一致性，纜繩受阻力的計算上，隨摩擦力係數的增加在共振頻率處會發生更大的能量損失，且慣性力係數對能量損失的改變輕微，而結構物的運動振幅於共振頻率處隨阻力的增加而減小。對波浪與纜繩錨碇浮式結構物互相作用的問題，本研究將纜繩分成有限個單元彈性體，且其運動方程式以Hamilton虛功法表示，考慮纜繩單元為小變形，將線性相對應變代入，則可得線性化的彈性單元運動方程式，以元素的概念引入，則可得纜繩有限元素法的質量矩陣、剛度矩陣與外力矩陣，其中外力包含纜繩的Morison波力與繫留力，利用繫纜點的邊界條件、合併浮式結構物與纜繩的運動方程聯立求解，本研究與Sannasiraj et al. (1998)的實驗結果相互比較顯示有良好的一致性，在轉動的自然頻率處，轉動對於水平運動會產生影響，波浪對纜繩的阻力在垂直運動與轉動的自然頻率處具有的影響，且對於轉動方向的運動，其能量的消散有顯著的效益。

This study developed an analytical solution in the frequency domain that considers the interactions among waves, floating structures, and mooring lines. The proposed solution was applied to investigate a problem involving a moored floating structure subjected to incident waves. The floating structure was considered as moving with three degrees of freedom, namely surge, heave, and roll. The mooring lines were simplified as springs, and the springs were assumed to be subjected to a Morison-type wave force. In the proposed solution, the wave field is first expressed as a problem involving a superposition of scattering and radiation waves. The wave field to be solved is expressed in terms of unknown structural motions, and wave forces acting on the floating structure and mooring springs are expressed in terms of the unknown wave fields. The solution to the coupling problem is obtained by solving the equations of motion of the floating structure with moorings. The proposed solution was simplified for evaluating cases without moorings, and its results are consistent with those of a solution in the literature. The presented solution was also used to investigate the effects of the mooring springs with added wave forces on wave fields and structural motions. The resonant amplitudes associated with the structure’s motion decreased, and the peaks of resonant frequencies shifted slightly toward lower frequencies. The added mass and radiation damping coefficients versus dimensionless wave frequencies are also presented.

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