Nonlinear hydroelastic interaction among a floating elastic plate, a train of deepwater waves, and a current which decays exponentially with depth is studied analytically. We introduce a stream function to obtain the governing equation with the dynamic boundary condition expressing a balance among the hydrodynamic, the shear currents, elastic, and inertial forces. We use the Dubreil-Jacotin transformation to reformulate the unknown free surface as a fixed location in the calculations. The convergent analytical series solutions for the floating plate deflection are obtained with the aid of the homotopy analysis method (HAM). The effects of the shear current are discussed in detail. It is found that the phase speed decreases with the increase of the vorticity parameter in the opposing current, while the phase speed increases with the increase of the vorticity parameter in the aiding current. Larger vorticity tends to increase the horizontal velocity. In the opposing current, the horizontal velocity under the wave crest delays more quickly as the depth increases than that of waves under the wave trough, while in the aiding current case, there is the opposite effect. Furthermore, the larger vorticity can sharpen the hydroelastic wave crest and smooth the trough on an opposing current, while it produces an opposite effect on an aiding current.

中文翻译：

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浮动弹性板，水波和指数剪切电流之间的非线性水弹性相互作用

通过分析研究了浮动弹性板，一系列深水波以及随深度呈指数衰减的电流之间的非线性水弹性相互作用。我们引入一个流函数来获得具有动态边界条件的控制方程，该边界条件表示流体动力，剪切电流，弹性力和惯性力之间的平衡。在计算中，我们使用Dubreil-Jacotin变换将未知的自由表面重新构造为固定位置。借助同伦分析方法（HAM），获得了浮板挠度的收敛分析级数解。详细讨论了剪切电流的影响。发现在相反电流中相速度随着涡度参数的增加而减小，相速度随着辅助电流中涡度参数的增加而增加。较大的涡流往往会增加水平速度。在逆流中，随着深度的增加，波峰下方的水平速度比波谷下方的波浪的速度更快地延迟，而在辅助电流情况下，则相反。此外，较大的涡旋可以使水弹性波峰变尖并使反向电流上的波谷变平滑，而对辅助电流却产生相反的影响。有相反的效果。此外，较大的涡旋可以使水弹性波峰变尖并使反向电流上的波谷变平滑，而对辅助电流却产生相反的影响。有相反的效果。此外，较大的涡旋可以使水弹性波峰变尖并在反向电流上使波谷变平滑，同时对辅助电流产生相反的影响。