On the Transverse Vibrations of Strings and Beams on Semi-Infinite Domains
On the Transverse Vibrations of Strings and Beams on Semi-Infinite Domains
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DOI：
10.1016/j.piutam.2016.03.033
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
T. Akkaya;W. T. Horssen
中科院分区：
文献类型：
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作者：
T. Akkaya;W. T. Horssen
本文研究在一个方向上无限长的弦和梁的横向振动。这些振动问题可作为拉索风雨激振的一个模型。为了抑制弦（或梁）中的不希望的振动，在边界处使用阻尼器。本文的主要目的是显示如何解决这些字符串和梁问题的半无限域可以计算。我们使用D 'Alembert方法推导出x = 0时质量-弹簧-阻尼器系统上的线性弦问题的显式解，并使用拉普拉斯变换方法推导出x = 0时具有铰接、滑动、夹持或阻尼边界的横向振动梁问题的显式解。它将显示如何波反射不同类型的边界。
In this paper, we study the transverse vibrations of a string and of a beam which are infinitely long in one direction. These vibration problems can be used as a toy model for rain-wind induced oscillations of cables. In order to suppress undesired vibrations in the string (or beam), dampers are used at the boundary. The main aim of this paper is to show how solutions for these string and beam problems on a semi-infinite domain can be computed. We derive explicit solutions for a linear string problem which is attached to a mass-spring-dashpot system atx= 0 by using the D’Alembert method, and for a transversally vibrating beam problem which has a pinned, sliding, clamped or damping boundary, respectively, atx= 0 by using the method of Laplace transforms. It will be shown how waves are reflected for different types of boundaries.