This study develops new analytical solutions to water wave diffraction by vertical truncated cylinders in the context of linear potential theory. Three typical truncated surface-piercing cylinders, a submerged bottom-standing cylinder and a submerged floating cylinder are examined. The analytical solutions utilize the multi-term Galerkin method, which is able to model the cube-root singularity of fluid velocity near the edges of the truncated cylinders by expanding the fluid velocity into a set of basis function involving the Gegenbauer polynomials. The convergence of the present analytical solution is rapid, and a few truncated numbers in the series of the basis function can yield results of six-figure accuracy for wave forces and moments. The present solutions are in good agreement with those by a higher-order BEM (boundary element method) model. Comparisons between present results and experimental results in literature and results by Froude-Krylov theory are conducted. The variation of wave forces and moments with different parameters are presented. This study not only gives a new analytical approach to wave diffraction by truncated cylinders but also provides a reliable benchmark for numerical investigations of wave diffraction by structures.

在线性势理论的背景下，本研究为垂直截断圆柱体对水波衍射的分析提供了新的解析方法。检查了三个典型的截断的表面刺破圆柱体，一个浸没式底缸和一个浸入式浮动缸。分析解决方案利用了多项式Galerkin方法，该方法能够通过将流体速度扩展为包含Gegenbauer多项式的一组基函数来对截断圆柱体边缘附近的流体速度的立方根奇异性进行建模。本分析解决方案的收敛速度很快，并且一系列基函数中的一些截断数可以得出波浪力和力矩的六位数精度结果。本解决方案与高阶BEM（边界元方法）模型的解决方案非常吻合。比较了目前的结果和文献中的实验结果以及根据Froude-Krylov理论得出的结果。给出了波浪力和力矩随不同参数的变化。这项研究不仅为平截圆柱体的波衍射提供了一种新的分析方法，而且为结构波衍射的数值研究提供了可靠的基准。