二维移动载荷引起漂浮板的非定常水弹性波阻和波形研究

Unsteady hydro-elastic wave resistances and deflections due to two-dimensional load moving on a floating plate

该文解析研究了漂浮在无限深无黏流体的无限长弹性板受二维移动载荷作用下变形以及载荷所受阻力。移动载荷分匀速运动和突然启动两种形式;使用Fourier积分变换法,得到积分形式解;对匀速运动的情况,采用留数定理得到波阻和波形的稳态解。结果发现:当载荷移动速度小于最小相速度时,无挠曲重力波波阻产生,稳态波形与静载下板的挠度分布相似;载荷速度大于最小相速度时,波阻存在并随移动速度的增加而呈现先增后减的趋势,挠曲波和重力波分别存在于前导区和后尾区。对于突然启动载荷的情况,水弹性响应包括稳态和瞬态两部分。使用驻相法得到瞬态波阻和波形渐近解。结果显示,瞬态动力特性依赖于载荷速度和最小群速度的关系,波阻和波形均随时间的增长而衰减,系统达到稳态。

The wave resistances and deflections due to a two-dimensional load moving on a thin elastic plate floating on an inviscid fluid of infinite depth are analytically studied. Uniformly moving and impulsively starting loads are considered. The integral solutions are obtained by the Fourier integral transform. For the motion due to a uniformly moving load, the steady-state solution for the wave resistances and deflections are deduced with the aid of residue theorem. It is found that when the moving speed of the load is less than the minimal phase speed, there is no wave resistance and the plate deflections are similar to those due to a static load. When the moving speed of the load is larger than the minimal phase speed, the wave resistance first increases to a peak and then decreases as the moving speed increases. The flexural and gravity waves are generated in the leading and trailing regions, respectively. For the motion due to an impulsively starting load, the response consists of the steady-state and transient components. The transient wave resistances and deflections are derived by means of the method of stationary phase. It is found that the transient behavior depends on the relation between the moving speed and the minimal group velocity. The transient wave resistances and deflections decay as the time increases and then a steady-state will be attained.