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Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

机译:斜入射波与两层流体上的半无限弹性板之间的水弹性相互作用

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The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural-gravity waves in a two-layer fluid and Snell's law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.
机译:研究了斜入射波引起的漂浮在有限深度两层流体上的半无限薄弹性板的水弹性响应。假定通过尖锐且稳定的界面分隔的具有不同密度的上,下流体是不粘且不可压缩的,并且运动是不旋转的。在线性势流理论的框架内,仅考虑具有给定角频率的表面和界面波模式的时谐入射波。借助匹配的本征函数展开法和两层流体的内积,导出了级联线性方程组的封闭系统,以求解级数解的反射系数和透射系数。根据两层流体中重力波和挠曲重力波的色散关系和斯涅尔折射定律,我们获得了表面波模入射波的临界角和表面波模的入射波的三个临界角。界面波模式,与传播波的存在有关。系列解决方案的图形表示显示了水波和板之间的相互作用。研究了几种物理参数,包括流体的密度和深度比以及板的厚度,对板的波散射和水弹性响应的影响。发现板厚度的变化可以改变波数和临界角。密度比是影响界面波模式波数的主要因素。最后,考虑应力状态。

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