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首页> 外文期刊>Journal of Engineering Mechanics >Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape
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Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape

机译：一般梯形二维障碍物对线性长波反射的解析研究

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摘要

In this paper, an analytical solution for linear long-wave reflection by an obstacle of general trapezoidal shape is explored. A closed-form expression in terms of first and second kinds of Bessel functions is obtained for the wave reflection coefficient, which depends on the relative lengths of the two slopes and top of the obstacle as well as the depth ratios in front of and behind the obstacle versus that above the obstacle. The analytical solution obtained in this study finds a few well-known analytical solutions to be its special cases, which include the wave reflection from a rectangular obstacle, an infinite step, and an infinite step behind a linear slope. The present analytical solution, however, covers a much wider range of problems. It is found that the periodicity of the wave reflection coefficient as the function of the relative length of the obstacle remains when two slopes are present but with a reduced magnitude. The phenomenon of zero wave reflection from the structure is special to a rectangular obstacle only, which disappears with the addition of a slope in front or at the rear. The new solution may be very useful in some engineering applications, for example, the design of a submerged breakwater of trapezoidal shape.
机译：本文探讨了一般梯形障碍物对线性长波反射的解析解。对于波反射系数，获得了根据第一类和第二类贝塞尔函数的闭式表达式，该表达式取决于两个坡度和障碍物顶部的相对长度以及前后的深度比。障碍与障碍之上。本研究中获得的解析解发现了几种众所周知的解析解作为其特例，包括矩形障碍物的波反射，无限阶跃和线性斜率后面的无限阶跃。但是，当前的分析解决方案涵盖了范围广泛的问题。发现当存在两个斜率但幅度减小时，波反射系数的周期性作为障碍物相对长度的函数而保留。从结构反射的零波现象仅对矩形障碍物是特殊的，随着前面或后面的倾斜而消失。新解决方案在某些工程应用中可能非常有用，例如，梯形淹没式防波堤的设计。

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