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A Large Span Crossbeam Vibration Frequencies Analysis Based on an Analogous Beam Method

机译：基于相似波束法的大跨横梁振动频率分析

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摘要

The novel method of an analogous beam is studied, which the flexural rigidity and mass per unit length correspond was described as the reciprocal of the mass per unit and the reciprocal of the flexural rigidity of the beam. It is shown that both beams possess the same natural frequencies of flexural vibration. In order to approximate calculation of these frequencies, the continuously distributed mass of the original beam is substituted for a number of concentrated masses. The analogous beam then becomes a chain of rigid links connected by pins and equipped with springs restraining the relative rotation of adjacent links. The equations of motion for the analogous beam can be solved by a procedure which consists of assuming a value for the natural frequency and calculating the deflections successively from one end of the beam to the other. Under normal circumstances, there will be a certain error, and one boundary condition will not be satisfied. The procedure is repeated with different values of the frequency until the error is removed. The method is illustrated by an example of a Crossbeam for which the fundamental frequency is found.
机译：研究了一种类似梁的新颖方法，将其抗弯刚度与单位长度质量相对应，描述为梁的单位质量与质量的倒数。结果表明，两个梁都具有相同的挠曲振动固有频率。为了近似计算这些频率，将原始光束的连续分布质量替换为许多集中质量。然后，类似的梁变成一排刚性链节，这些链节通过销钉连接并配备有弹簧，用于限制相邻链节的相对旋转。类似光束的运动方程可以通过以下程序求解：该程序包括为固有频率取一个值，然后依次计算从光束一端到另一端的挠度。通常情况下，会有一定的误差，并且不能满足一个边界条件。以不同的频率值重复该过程，直到错误消除。该方法以找到其基本频率的交叉光束的示例进行说明。

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  • 来源
    《Mathematical Problems in Engineering》 |2013年第1期|247268.1-247268.9|共9页
  • 作者

    Zhifeng Liu; Bing Luo; Yongsheng Zhao; Wentong Yang; Ligang Cai;

  • 作者单位

    College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;

    College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;

    College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;

    College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;

    College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, China;

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