具有周期边界的弯曲散射问题的积分方程
Integral equations for flexural scattering problems with periodic boundaries
AI总结：
本文提出了一种基于准周期性弯曲格林函数的积分方程方法，用于高效求解具有周期边界的弯曲波散射问题。
摘要：
我们开发了一种计算周期壁或周期散射线附近弯曲波散射的方法。这些波模型了具有周期固定、支撑或自由边的薄板的波动。我们使用Floquet-Bloch变换将问题转换为一组解耦的准周期性问题。然后我们利用基于准周期性弯曲格林函数的新积分方程高效准确地求解每个准周期性问题。最后，我们展示了该方法如何用于模拟半无限散射线交汇处的散射。
英文摘要：
We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with periodic clamped, supported, or free edges. We use the Floquet-Bloch transform to convert the problem into a collection of uncoupled quasi-periodic problems. We then solve each quasi-periodic problem efficiently and accurately using a novel integral equation based on the quasi-periodic flexural Green's function. Finally, we show how the proposed method can be used to simulate scattering from junctions of semi-infinite lines of scatterers.
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