可压缩性水柱冲击弹性平板的砰击问题研究

摘要

文章采用一种将波动控制方程进行双重渐进近似的方法研究可压缩性水柱砰击弹性平板问题。文中用边界元法对控制方程进行离散，并使用非线性的运动学以及动力学边界条件更新未知的自由液面。在相同的线性边界条件下，将数值计算结果与Korobkin（2008）给出的解析解进行对比，研究双重渐进近似对数值计算结果的影响，同时验证了该方法的正确性。结果表明数值解和解析解吻合良好。在此基础上，研究非线性边界条件对弹性板中心的位移以及压力的影响，并进行了深入的讨论。%A doubly asymptotic approximation for the governing wave equation was adopted to study the initial impact problem of a compressible water column on an elastic plate. The governing equation is solved by a boundary element method and non-linear boundary conditions are used to update the unknown free surface. Numerical results are compared with analytic solutions by Korobkin (2008) un-der the same linear boundary conditions, to study the influence of the doubly asymptotic approxima-tion on the numerical results and testify its accuracy, which shows that good agreements are found. The influence of the non-linear boundary conditions on the displacements and the pressure of the plate center is analyzed and discussed.