This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is recast into a coupled boundary value problem for the Helmholtz and modified Helmholtz equations. A novel boundary integral formulation is proposed for the coupled problem. By introducing an appropriate regularizer, the well-posedness is established for the system of boundary integral equations. Moreover, the convergence analysis is carried out for the semi- and full-discrete schemes of the boundary integral system by using the collocation method. Numerical results show that the proposed method is highly accurate for both smooth and nonsmooth examples.

翻译：本文涉及一个无限薄板的洞穴散射问题,在这种盘子里,飞机外移位由二维双调波方程式管理。在操作员分裂的基础上,散移问题被重新分为Helmholtz和修改Helmholtz等式的混合边界值问题。为混合问题提出了一个新的边界整体配方。通过引入适当的调制器,为边界整体方程式系统确定了良好的保质性。此外,还利用合用法对边界整体系统的半分和完全分立办法进行了趋同分析。数字结果显示,拟议的方法对于光滑和非移动的例子都是非常准确的。