波流与不均匀海域上浮式弹性板相互作用的非线性数值模拟

Nonlinear numerical simulation for wave-current interaction with a floating elastic plate over variable depth sea bottom

波流混合作用下浮式弹性板的水弹性响应属于非线性范畴,尤其当波流传递到不均匀海底时,这种非线性行为更为复杂,因而采用完全非线性分析技术是唯一可能获得浮板精确水弹性响应的方法。采用高阶边界元法建立模拟波流与变水深海底上浮板相互作用的时域完全非线性二维数值水槽;将Euler-Bernoulli-von Karman非线性梁模型加入到流固交界面的动力学边界条件中实现波流与浮板耦合作用,运用4阶Runge-Kutta法并联合混合欧拉-拉格朗日方案对瞬时自由水面和流固交界面进行更新;为获得浮板位移的空间各阶导数,使用一系列模态振型函数来近似当前时刻浮板的垂向位移,并利用Galerkin方法求解各阶模态主坐标。通过与无网格数值已知算法结果进行比较,验证了数值模型的可行性和准确性;进一步研究水流及不均匀海底的存在对浮板非线性水弹性响应产生的影响;最后探讨了不同流速对浮板高阶谐位移的影响规律。

Hydroelastic analysis of wave-current nonlinear interaction with a floating elastic plate is complex, specially when water waves propagate along uneven sea bottom. The fully nonlinear analysis techniques are widely ecognized as a unique approach to predict the accurate hydroelastic responses. A 2D （two-dimensional） time domain ully nonlinear numerical tank using higher-order boundary element method was devoted to solve such a problem in this ork. The fourth-order Runge-Kutta time stepping integration scheme with the mixed Eulerian-Lagrangian approach was pplied to update the instantaneous free and plate surface. An Euler-Bemoulli-von Karman nonlinear beam model was ntroduced to determine the fluid pressure imposed on the fluid-structure interface. In order to obtain derivatives of plate urface, the plate displacement was interpolated using a series of modal functions, and the modal amplitudes were solved y applying the Galerkin scheme. The numerical solutions were validated against existing meshless numerical results. urther calculations were then conducted to examine the effects of currents and the uneven topography on the displacement onlinearity of the plate. Finally, the higher harmonic displacements were investigated with the various current velocities.