This paper treats a pipe as a beam or as a thin shell. Then, the effect of cracks on the dynamic characteristics of pipes is calculated by means of the model of zero dimension element with crack.

在考虑管道长度特征的前提下，把管道近似地看作长梁或薄壳，然后以“含裂纹零维度单元”模型（即垂直于裂纹面方向的单元尺度为零）计算出裂纹对管道动态特性的影响。

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