标题： Lamb问题的精确闭式解（II）：移动点载荷 显示英文标题

标题： Exact closed-form solutions for Lamb's problem (II): a moving point load

摘要： 本文报告了弹性均匀半空间在向下垂直点源作用下因表面介质以恒定速度移动而产生的位移的精确闭式解。 这里考虑的问题是对Lamb问题的扩展。 从Bakker的积分解\textit{等}出发，我们采用了Feng和Zhang提出的方法，该方法专注于固定点源在自由表面上引起的位移，从而得到了最终以基本代数函数以及第一、第二和第三类椭圆积分表示的解。 我们的闭式结果与Bakker的数值结果\textit{等}完全一致，这验证了我们公式的正确性。 本文所获得的解可能为进一步考虑实际物理移动载荷（如高速铁路列车）的响应奠定坚实的基础。 显示英文摘要

摘要： In this article, we report on an exact closed-form solution for the displacement in an elastic homogeneous half-space elicited by a downward vertical point source moving with constant velocity over the surface of the medium. The problem considered here is an extension to Lamb's problem. Starting with the integral solutions of Bakker \textit{et al.}, we followed the method developed in Feng and Zhang, which focuses on the displacement triggered by a fixed point source observed on the free surface, to obtain the final solution in terms of elementary algebraic functions as well as elliptic integrals of the first, second and third kind. Our closed-form results agree perfectly with the numerical results of Bakker \textit{et al.}, which confirms the correctness of our formulas. The solution obtained in this article may lay a solid foundation for further consideration of the response of an actual physical moving load, such as a high-speed rail train.