海洋浮体二阶非线性水弹性力学分析—基本理论

Second Order Nonlinear Hydroelastic Analyses of Floating Bodies - Theory

将考虑到二阶的流场压力在浮体瞬时湿表面上积分 ,得到用于非线性水弹性理论分析的广义一阶流体作用力和广义二阶流体作用力。广义一阶流体作用力中的波浪激励力、辐射力和恢复力与线性水弹性理论中的广义流体力具有相同的形式 ,仅比线性水弹性理论多了一项 ,反映了由刚体的转动引起的对一阶流体恢复力的影响。广义二阶流体力由五部分组成 ,即 :与入射势和反射势有关的广义二阶波浪激励力、与辐射势有关的广义二阶辐射力、由辐射势与入射势及反射势的耦合引起的广义二阶力、由于湿表面的移动引起的一阶流场静态压力对广义二阶流体力的贡献、以及由于瞬时湿表面积的变化引起的广义二阶力。同时推导了不规则波中的广义一阶及二阶流体动力系数的表达形式。建立了在不规则波中航行浮体的线性和非线性水弹性运动方程 ,给出了求解方法。

By integration of the second-order fluid pressure over the instantaneous wetted surface,the generalized first-and second-order fluid forces needed in nonlinear hydroelastic analysis are obtained.The generalized first order wave exciting forces,radiation forces and restoring forces have the same form as in linear hydroelasticity theory.One added first-order term represents the influence of the rigid body rotations to the first-order forces in the nonlinear analysis.The generalized second-order fluid forces consist of five parts:generalized second-order wave exciting forces which are related to incident and diffracted wave potentials;generalized second-order radiation forces related to radiation potentials;generalized second-order forces induced by the coupling between radiation wave potentials and incident-diffracted wave potentials;generalized second-order forces induced by the movement of wetted surface;and generalized second-order forces induced by the instantaneous variation of the wetted surface.The expressions for coefficients of the generalized first-and second-order hydrodynamic forces in irregular waves are also given.Based on these,the nonlinear hydroelasticity equations for arbitrary floating bodies in irregular waves are presented,and the solution method is discussed.Numerical results of the second-order nonlinear hydroelastic analysis of ocean floating systems will be given in the accompanying paper.