柱形地形上单浮体的辐射和散射问题

On Scattering and Radiation Problem for a Cylinder over a Cylindrical Barrier in Water of Finite Depth

在有限水深、同轴但半径大于或等于浮体半径的圆柱体障碍物地形条件下 ,基于特征函数展开法 ,推导了垂直放置的圆柱形浮体由于波的辐射和散射作用所表现的动力学和运动学特征表达式 ,涉及浮体做垂荡、横荡和横摇运动所产生的辐射势 ,以及在入射波的作用下 ,由于浮体固定不动而产生的散射势 ,并推导了激励力、附加质量和阻尼系数表达式。采用与同轴、同半径圆柱体障碍物地形上单浮体水动力学特性相比的方式和激励力计算两种方法验证了推导的表达式 。

By use of an eigenfunction expansion method, the expressions for the properties of kinematics and kinetics, which are due to scattering and radiation for a floating vertical circular cylinder over a coaxial cylindrical barrier in water of finite depth, are derived in the presence of an incident linear waves. The radius of the barrier is larger than or equal to that of the floating vertical circular cylinder. This paper presents the analytical solution for the radiation potentials due to heave, surge, and pitch and for the diffraction potential due to the diffraction of an incident wave acting on the fixed cylinder. It also proposes a set of theoretical added masses, damping coefficients and exciting forces. The results of the expressions are the same as that of the cylinder over a cylindrical barrier, the radius of wich is the same as that of the cylinder, in water of finite depth for added masses, damping coefficients and exciting forces at the same condition. Two methods to calculate exciting forces are presented and the results of the methods are the same. Finally, Analytical results of added masses, damping coefficients and exciting forces are obtained for different size of the barrier.