Water wave scattering by two asymmetric thin elastic plates with arbitrary inclinations is investigated using integral equations. The plates are submerged in finite depth water. The assumption of Euler–Bernoulli beam model for the plates, the use of the appropriate Euclidean transformations to handle the fifth-order plate conditions and the application of Green’s function technique allow us to obtain the expressions of normal velocities at arbitrary points over the plates. On the other hand, an application of Green’s integral theorem on the scattered potential and the source potential functions gives us the alternative expressions of the above-mentioned normal velocities. The comparison of these alternative forms provides two coupled integral equations involving the unknown potential differences across the plates. Kernels of the integral equations have regular as well as hypersingular parts so that the resulting integral equations are hypersingular in nature. These are solved numerically and the solutions are utilized to compute the numerical estimates for different physical quantities. Published results are recovered for different arrangements of the plates and new results are presented graphically for various parametric values.

中文翻译：

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表面波通过非对称弹性板的传播

使用积分方程研究了具有任意倾角的两个不对称薄弹性板的水波散射。这些板块被淹没在有限深度的水中。板的欧拉-伯努利梁模型的假设，使用适当的欧几里得变换来处理五阶板条件以及格林函数技术的应用，使我们能够获得板上任意点的法向速度表达式。另一方面，格林积分定理在散射势函数和源势函数上的应用为我们提供了上述法向速度的替代表达式。这些替代形式的比较提供了两个耦合积分方程，其中涉及跨板的未知电位差。积分方程的核具有正则和超奇异部分，因此所得积分方程本质上是超奇异的。这些都被数​​值求解，并利用这些解来计算不同物理量的数值估计。已发布的结果可针对不同的板排列进行恢复，并以图形方式呈现各种参数值的新结果。