Smith M J A, Peter M A, Abrahams I D, Meylan M H
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany.
Proc Math Phys Eng Sci. 2020 Oct;476(2242):20200360. doi: 10.1098/rspa.2020.0360. Epub 2020 Oct 28.
A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener-Hopf technique. The derivation of the Wiener-Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.
利用维纳-霍普夫技术，给出了由半无限大浸没薄弹性板（多孔或无孔）引起的水波散射问题的一个解。维纳-霍普夫方程的推导与传统水波问题中使用的推导有很大不同，它直接导出了所需的方程。还展示了如何使用柯西型积分直接计算该解，这避免了求解高度复杂的色散方程的根的需要。我们通过一些数值计算来说明该方法，重点关注入射波脉冲的演化，这说明了浸没板系统中存在两个透射波。研究了孔隙率的影响，结果表明它对短波长脉冲的影响比对长波长脉冲的影响要强得多。
