A three‐dimensional problem of wave diffraction by a neutrally buoyant immersed sphere in a fluid having a flexible bottom surface is studied within the framework of linear potential theory. The flexible base surface of the fluid is modelled as a narrow flexible sheet and it follows on the Euler‐Bernoulli bar condition. The impact of the free‐surface tension is ignored. In such circumstances, the time‐harmonic proliferating waves with two distinct wavenumbers propagate in the fluid for any specific frequency. The proliferating waves having higher wavenumber spread along the flexible bottom surface, say, flexural mode and the proliferating waves having smaller wavenumber spread along the free‐surface of the fluid, say, free‐surface mode. By applying the multipole technique, we acquire the analytical solution for the issue of wave diffraction by a rigid sphere immersed in a fluid having flexible bottom surface. This technique reduces the boundary value problem to the solution of an infinite number of algebraic linear non‐homogeneous equations which can easily resolve numerically by any conventional technique. The exciting forces acting on the submerged sphere along the horizontal and vertical directions in the fluid are estimated in the case of both the flexural and free‐surface wave modes. These forces are plotted graphically for several immersion depths of the rigid sphere and the rigidity factors of the flexible base surface of the fluid.

中文翻译：

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具有柔性基础表面的流体中作用于刚性球体的激振力的分析研究

在线性势能理论的框架内研究了中性浮力沉浸球在具有柔性底表面的流体中的三维衍射问题。流体的柔性基础表面被建模为狭窄的柔性板，并且遵循欧拉-伯努利杆条件。自由表面张力的影响被忽略。在这种情况下，具有两个不同波数的时谐扩散波以任何特定频率在流体中传播。波数较高的扩散波沿挠性底面传播，即弯曲模式，波数较小的扩散波沿流体的自由面传播，即自由表面模式。通过应用多极技术，我们获得了通过将刚性球体浸入具有柔性底面的流体中而产生的波衍射问题的解析解。该技术将边界值问题简化为无数个代数线性非齐次方程的解决方案，这些问题可以通过任何常规技术轻松地进行数值求解。在弯曲波模式和自由表面波模式的情况下，均会估计沿流体的水平和垂直方向作用于水下球体的激励力。对于刚性球体的几个浸入深度和流体柔性基面的刚度系数，这些力以图形方式绘制。该技术将边界值问题简化为无数个代数线性非齐次方程的解决方案，这些问题可以通过任何常规技术轻松地进行数值求解。在弯曲波模式和自由表面波模式的情况下，均会估计沿流体的水平和垂直方向作用于水下球体的激励力。对于刚性球体的几个浸入深度和流体柔性基面的刚度系数，这些力以图形方式绘制。该技术将边界值问题简化为无数个代数线性非齐次方程的解决方案，这些问题可以通过任何常规技术轻松地进行数值求解。在弯曲波模式和自由表面波模式的情况下，均会估计沿流体的水平和垂直方向作用于水下球体的激励力。对于刚性球体的几个浸入深度和流体柔性基面的刚度系数，这些力以图形方式绘制。