沉箱上单浮体流体动力学问题的解析方法

Analytical Method of Hydrodynamic Problem for Cylinder Over Caisson in Water of Finite Depth

在有限常水深、同轴同半径圆柱体沉箱条件下,基于特征函数展开法,推导了垂直放置的圆柱形浮体在水波作用下所受到流体作用力表达式.涉及了浮体做垂荡、纵荡和纵摇运动相关联的辐射势,以及在入射波的作用下由于浮体固定不动而相关联的绕射势.还推导了激励力、附加质量和阻尼系数表达式,采用同平底单浮体运动条件相比和激励力计算的两种方法的方式验证了推导的表达式.最后分析了沉箱高度对浮体运动的特有影响,在算例范围内沉箱的高度对垂荡、纵摇运动的影响较大,对纵荡运动的影响较小.

By means of an eigenfunction expansion method,the expressions for the hydrodynamic problem arising diffraction and radiation for a floating vertical circular cylinder over a coaxial cylindrical caisson in water of finite depth are derived in the presence of incident linear waves.The radius of the caisson is the same as that of the floating vertical circular cylinder.The analytical solution is presented 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,and a set of theoretical added masses,damping coefficients and exciting forces is proposed.The results of the expressions is the same as that of the cylinder in water of finite depth for added masses,damping coefficients and exciting forces under the same condition.Two methods are presented to calculate exciting forces and the results of the methods are the same.Finally,analytical results of added masses,damping coefficients and exciting forces are obtained for different depths of the caisson.In calculating the example range,it is concluded that the effect of the caisson on the heave and pitch motions of the cylinder is obvious but not so noticeable on the surge motion.