本文對於週期波浪作用於浮式結構物時，波浪場與結構物運動行為的描述，提出線性化的理論解析解。文中考慮垂直平面之二維波浪場中，一具有水平(surge)、上下(heave)、轉動(pitch)等三個運動自由度的不透水矩形浮式結構物，將入射波引發結構物運動的完整敘述，利用Sarpakaya(1981)的求解概念，分為散射問題與單位振幅結構物運動之輻射問題，最後以結構物運動方程式求解整個問題。其中散射問題、結構物水平運動之輻射問題、結構物垂直運動之輻射問題的求解過程，在文獻中已有完整敘述，本文主要提出單位振幅結構物往復轉動之輻射問題的理論解析過程，並且結合散射問題與三個輻射問題來描述結構物運動。求解單位振幅結構物轉動之輻射問題時，假設結構物轉動角度極小，利用具有梯度的移動邊界來模擬轉動行為，並且利用Lee(1995)提出的求解方式，處理結構物下方具有非齊性邊界的流場。上述散射問題與幅輻射問題的解析結果，配合結構物運動方程式，便可得到浮式結構物與波浪互相作用的理論解析解。

The purpose of this study is to present a theoretical solution for the linearlized problem of incident waves acting on a floating structure. The problem considered is two-dimensional vertically, the floating structure is rectangular, and the motion is of three degrees of freedom. The solution concepts used in this study follow that presented by Sarpkaya (1981), in which the problem is separated into a scattering problem and radiation problems with unit motion amplitude, and the problem is finally solved by using equations of motion of the floating structure. Analytic solutions for the scattering problem, radiation problems of horizontal motion (surge) and vertical motion (heave) have already shown in the literature. Main contributions of this study are that the radiation problem of the rotational motion (pitch) with unit amplitude is proposed first, and motions of the floating structure with three degrees of freedom are solved theoretically. In the solution of rotational radiation problem, the boundary value problem with nonhomogeneous boundary condition beneath the structure is solved by using a solution procedure proposed by Lee (1995). By combining the scattering solution, radiation solutions of three degrees of freedom, and equations of motion of the floating structure, an analytic solution for the problem is developed.

1. Black, J.L., Bray, M.C.G. and Mei, C.C., “Radiation and scattering of water waves by rigid bodies,” Journal of Fluid Mechanics, Vol. 46, Part.1, pp. 151-164, 1971.
2. Huang, M.C., “Finite element analysis of wave interference effects between large structures,” Ph.D. Thesis, Oregon State University, Oregon, 1982.
3. Ijima, T., Tabuchi, Y. and Yumura, Y., “Scattering of surface waves and the motions of a rectangular body by waves in finite water depth,” Proceedings of Japan Society of Civil Engineers, No. 202, pp. 33-48, June, 1972.
4. Lee, C.P., Lee, J.F., “Wave-induced surge motion of a tension leg structure,” Ocean Engineering, Vol. 20, No. 2, pp. 171-186, 1993.
5. Lee, J.F., “On the heave radiation of a rectangular structure,” Ocean Engineering, Vol. 22, No. 1, pp. 19-34, 1995.
6. Mei, C.C., “The applied dynamics of ocean surface waves,” John Wiley& Sons, Inc., New York, 1983.
7. Sarpkaya, T., Isaacson, M., “Mechanics of wave forces on offshore structures,” Van Nostrand Reihold Co., 1981.
8. 李兆芳, 海洋結構物波力計算, 海岸工程學, 295頁-323頁, 2001。