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首页> 外文期刊>Journal of Sound and Vibration >An approximate method for determining the static deflection and natural frequency of a cracked beam
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An approximate method for determining the static deflection and natural frequency of a cracked beam

机译：确定裂纹梁的静挠度和固有频率的一种近似方法

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摘要

This paper provides an approximate method to determine the stiffness and the fundamental frequency of a cracked beam. The cracked beam is first represented as an un-cracked beam with equivalent reduced sections around the cracks. The effect of the cracks is explained, visualised and quantified using the equivalence concept developed for stepped beams with periodically variable cross-sections. Then an alternative expression of the improved Rayleigh method is provided to calculate the natural frequencies of a beam with a variable stiffness distribution along its length. As the method is insensitive to the assumed mode shapes, it avoids the difficulty in choosing appropriate mode shapes and yields accurate results. This is shown using several examples to compare the results determined using the proposed method and the Finite Element method (FEM). The method greatly simplifies the calculation of cracked beams with complicated configurations, such as a beam with several cracks, a cracked beam with concentrated masses, a beam with cracks close to each other, and a beam with periodically distributed cracks.
机译：本文提供了一种确定破裂梁的刚度和基频的近似方法。首先将裂痕束表示为未裂痕束，其具有围绕裂痕的等效减小的截面。使用针对具有周期性变化的横截面的阶梯梁开发的等效概念来解释，可视化和量化裂纹的影响。然后，提供了改进的瑞利方法的替代表达式，以计算沿其长度具有可变刚度分布的梁的固有频率。由于该方法对假定的模态形状不敏感，因此避免了选择合适模态形状的困难，并产生了准确的结果。使用几个示例显示了这一点，以比较使用建议方法和有限元方法（FEM）确定的结果。该方法大大简化了具有复杂构造的裂纹束的计算，例如具有多个裂纹的束，具有集中质量的裂纹束，彼此靠近的裂纹束以及周期性分布的裂纹束。

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