半有界弦末端消去反射波的运动规律

Kholodovskii Svyatoslav Ye.
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引用次数: 0

摘要

考虑半有界弦在给定初始扰动'(x)下,弦的左端按给定规律f(t)运动时(t时间)的振荡问题。对于任意函数'(x)和f(t),得到了问题的最终解。构造了构成结果波的弦的正、逆和反射波分量。研究了函数f(t)对反射波振幅的影响。对于弦的任意初始扰动,我们发现了弦末端的运动规律,在那里反射波消失。本文的相关性是由与扩展物体(桥梁、梁、天线)振动相关的广泛实际问题决定的,当运动源是初始扰动和施加在物体末端的给定外力时。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Law of Motion of the End of a Semi-Bounded String, Which Extinguishes Reflected Waves
The problem of oscillation of a semi-bounded string at a given initial perturbation '(x), when the left end of the string moves according to a given law f(t), is considered (t time). The solution of the problem is obtained in the final form for arbitrary functions '(x) and f(t). The direct, inverse and reflected from the end of the string wave components that make up the resulting waves are constructed. The influence of the function f(t) on the magnitude of the reflected waves is investigated. For an arbitrary initial perturbation of a string, the law of motion of its end is found, at which the reflected waves disappear. The relevance of the article is determined by a wide range of practical problems related to the vibrations of extended objects (bridges, beams, antennas), when the source of motion is an initial perturbation and a given external force applied to the end of the object.
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