Vibrations of double-string complex system under moving forces. Closed solutions
Vibrations of double-string complex system under moving forces. Closed solutions
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DOI：
10.1016/j.jsv.2010.08.021
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发表时间：
2011-01
影响因子：
4.7
通讯作者：
J. Rusin;Piotr Śniady;Piotr Śniady
中科院分区：
文献类型：
--
作者：
J. Rusin;Piotr Śniady;Piotr Śniady
本文研究了双弦系统在常激振力或简谐激振力作用下的动力响应。力以恒定的速度作用在最上面的弦上。弦是相同的，平行的，一个在另一个上，并通过线性Winkler弹性元件连续耦合。双弦系统在匀速运动力作用下响应的经典解具有无穷级数的形式。本文的主要目标是表明，在所考虑的情况下，解决方案的一部分，可以在一个封闭的，分析的形式，而不是一个无穷级数。所提出的方法找到一个封闭的，分析形式的解决方案是基于观察到的解决方案的系统的偏微分方程的形式的一个无穷级数也是一个解决方案的一个适当的系统的常微分方程。
In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.