本研究以理論解析探討波浪與水中錨碇浮式結構物互相作用問題，波浪以線性勢能波理論描述，考慮二維結構物含有三個自由度的運動，包含水平(surge)、垂直(heave)和轉動(pitch)，錨碇系統則以線性彈簧進行模擬，同時特別考慮作用於錨碇系統上之波力。在求解作法上，首先將波浪勢函數分解為散射波與三個自由度的結構物單位振幅輻射波，接著建立水中結構物運動方程式，其中外力項包含入射波、散射波與輻射波作用於結構物上之波力、錨碇系統提供之繫留力以及利用Morison公式計算作用於錨碇系統上之波力，繫留力即為彈簧回復力，可視為勁度矩陣加入結構物運動方程式中，最後求解結構物運動方程式得到結構物運動振幅，並同時得到互相作用後之波浪場。利用本理論模式可探討不同結構物尺寸對於波浪場之影響，以及結構物運動特性。由計算結果發現在結構物運動共振頻率處將產生反射率最大值，而結構物轉動與水平運動將相互影響，而彈簧上波力效應則在結構物共振頻率特別顯著，彈簧上形狀阻力將消散系統的能量。

本研究除提出一理論模式外，也建立數值模式來求解相同問題，利用邊界元素法(BEM)求解波浪場。將數值計算結果提供理論模式作為比較對象，結果顯示理論解和數值解有很好的一致性，雖然數值模式計算時間較長，但後續可延伸探討任意形狀之結構物，理論解析則受限於規則幾何之型態。

The coupling problem of wave acting on an underwater floating structure with moorings is solved analytically in this research. The water wave motion is described via linear potential wave theory. Motions of a two-dimensional structure possess three-degrees of freedom: surge, heave, and pitch. The anchor system is simulated by linear springs. The wave-structure interaction problem has the following features: (1) the wave potentials can be decomposed into scattered waves and three different radiation waves of unit amplitude. (2) the momentum equations of an underwater floating structure are established by calculating wave forces acting on floating structures, spring restoring forces, and wave forces acting on mooring lines. The latter ones can be calculated from the Morison equation. By solving the momentum equations of the floating body, the amplitudes of structural motions can be obtained and the complete wave fields can be determined at the same time. Based on present analytic solution, the effects of structural dimensions on the wave reflection coefficients and on structural motions are also investigated. The results show that the wave reflection coefficients have peak values at the resonant frequencies of structure motions. The effect of wave forces on mooring lines is significant at the appearance of the structure’s resonant frequency.

Besides the analytic solution, a numerical solution based on the boundary element method is presented. The two solutions show close agreement. The numerical model can be extended for arbitrary body shapes, while the analytic solution is limited to regular shapes.

1. Abull-Azm, A.G., and Gesraha, M.R., “Approximation to the hydrodynamics of floating pontoons under oblique waves”, Ocean Engineering, Vol. 27, Issue, 4, pp. 365-384, April, 2000.
2. Bai, W., and Taylor, R.E., “Fully nonlinear simulation of wave interaction with fixed and floating flared structures”, Ocean Engineering, Vol. 36, Issue, 3-4, pp. 223-236, March, 2009.
3. Brebbia, C.A. and Domingnez, J., “Boundary Elements an Introductory Course”, Second Edition, Computational Mechanics Publications, 1992.
4. Chen, P.I, Chen, C.T., and Lee, J.F., “On wave interaction with floating structures with dragged moorings”, Journal of Marine Science and Technology, Vol. 24, No. 4, pp. 530-538, June, 2016.
5. Chen, Z.J., Wang, Y.X., Dong, H.Y., and Zheng, B.X., “Time-domain hydrodynamic analysis of pontoon-plate floating breakwater”, Vol. 5, No. 3, pp. 291-303, September, 2012.
6. Cheong, H.F., Shankar, N.J., and Nallayarasu, S., “Analysis of submerged platform breakwater by eigenfunction expansion method”, Ocean Engineering, Vol. 23, No. 8, pp. 649-666, November, 1996.
7. Drimer, N., Agnon, Y., and Stiassnie, M., “A simplified analytical model for a floating breakwater in water of finite depth”, Applied Ocean Research, Vol. 14, pp. 33-41, 1992.
8. Dombre, E., Benoit, M., Violeau, D., Peyrard, C., and Grilli, S.T., “Simulation of floating structure dynamics in waves by implicit coupling of a fully non-linear potential flow model and a rigid body motion approach”, Journal of Ocean Engineering and Marine Energy, Vol. 1, Issue, 1, pp.55-76, February, 2015.
9. Elchahal, G., Younes, R., and Lafon, P., “Parametrical and motion analysis of a moored rectangular floating breakwater”, Offshore and Structural Mechanics, Vol. 131, August, 2009.
10. Hsu, H.H., and Wu, Y.C., “The hydrodynamic coefficients for an oscillating rectangular structure on a free surface with sidewall”, Ocean Engineering, Vol. 24, No. 2, pp. 177-199, February, 1997.
11. Jain, R.K., “A simple method of calculating the equivalent stiffenesses in mooring cables”, Vol. 2, Issue. 3, pp. 139-142, July, 1980.
12. Kim, B.W., Sung, H.G., Kim, J.H., and Hong, S.Y., “Comparison of linear spring and nonlinear FEM methods in dynamic coupled analysis of floating structure and mooring system”, Journal of Fluids and Structures, Vol. 42, pp. 205-227, October, 2013.
13. Lee, C.P. and Lee, J.F., “Wave-induced surge motion of a tension leg structure”, Ocean Engineering, Vol. 20, No. 2, pp. 171-186, 1993.
14. Lee, C.P., “Dragged surge motion of a tension leg structure,” Ocean Engineering”, Vol. 21, No. 3, pp. 311-328, 1994.
15. Lee, H.H., Wang, P.W. and Lee, C.P., “Dragged surge motion of tension leg platforms and strained elastic tethers”, Ocean Engineering, Vol. 26, No. 6, pp. 575-594, 1999.
16. Lee, H.H., Wang, P.W., “Dynamic behavior of tension-leg platform with net-cage system subjected to wave forces”, Ocean Engineering, Vol. 28, No. 2, pp. 179-200, January, 2001.
17. Lee, J.F., “On the heave radiation of a rectangular structure”, Ocean Engineering, Vol. 22, No.1, pp. 19-34, 1995.
18. Li, Y., and Lin, M., “Regular and irregular wave impacts on floating body”, Ocean Engineering, Vol. 42, pp.93-101, March, 2012.
19. Mei, C.C. and Black, J.L., “Scattering of surface waves by rectangular obstacles in waters of finite depth”, Journal of Fluid Mechanics, Great Britain, Vol. 38, part 3, pp. 499-511, 1969.
20. Mei, C.C., “The applied dynamics of ocean surface wave,” John Wiley& Sons, Inc., New York, 1983.
21. Ogawa, Y., “Fundamental analysis of deep sea mooring line in static equilibrium”, Applied Ocean Research, Vol. 6, Issue. 3, pp. 140-147, July, 1984.
22. Peng, W., Lee, K.H., Shin, S.H., and Mizutani, N., “Numerical simulation of interactions between water waves and inclined-moored submerged floating breakwaters”, Coastal Engineering, Vol. 82, pp. 76-87, December, 2013.
23. Rahman, M.A., Mizutani, N., and Kawasaki, K., “Numerical modeling of dynamic responses and mooring forces of submerged floating breakwater”, Coastal Engineering, Vol. 53, No. 10, pp. 799-815, September, 2006.
24. Sannasiraj, S.A., Sundar, V. and Sundaravadivelu, R., “Mooring forces and motion responses of pontoon-type floating breakwaters”, Ocean Engineering, Vol. 25, No. 1, pp. 27-48, January, 1998.
25. Williams, A.N., and McDougal, W.G., “A dynamic submerged breakwater”, Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 122, Issue 6, pp. 288-296, November, 1996.
26. Wu, C., Watanabe, E., and Utsunomiya, T., “An eigenfunction expansion-matching method for analyzing the wave-induced responses of an elastic floating plate”, Applied Ocean Research, Vol. 17, Issue 5, pp.301-310, October, 1995.
27. Yamamoto, T., Yoshida, A., and Ijima, T., “Dynamics of elastically moored floating objects”, Applied Ocean Research, Vol. 2, Issue 2, pp. 85-92, April, 1980.
28. Zheng, Y.H., Liu, P.F., Shen, Y.M., Wu, B.J., and Sheng, S.W., “On the radiation and diffraction of linear water waves by and infinitely long rectangular structure submerged on oblique seas”, Ocean Engineering, Vol. 34, No. 3-4, pp. 436-450, March, 2007.
29. Zheng, Y.H., You, Y.G., and Shen, Y.M., “On the radiation and diffraction of water waves by a rectangular buoy”, Vol. 31, No. 8-9, pp. 1063-1082, June, 2004.
30. 李兆芳，海洋結構物波力計算，海岸工程學，第295-232頁，2001。
31. 洪偉勝，波浪與浮式結構物互相作用之理論分析，碩士論文，國立成功大學水利及海洋工程學系研究所，2003。
32. 陳伯義、李兆芳、洪偉勝，波浪與浮式結構物互相作用之理論解析，海洋工程學刊，第6卷，第2期，第63-80頁，2006。