Abstract The efficiency and reliability of the bulb turbine can be influenced by the crack fault of the blade in the actual hydropower engineering. To explore this problem, this work is employed to mainly study the effects of the crack fault on the dynamic characteristics of the blade under different external excitations. Firstly, a displacement function of the cracked blade is innovatively proposed as the sum of a polynomial admissible function and a supplementary admissible function reflecting crack characteristics. Then, employing this displacement function, the natural frequency and mode function of the cracked blade can be calculated by Ritz method. Moreover, based on the derived mode function, the dynamical differential equation of the cracked blade can also be obtained. Finally, the truncation sensitivity of the displacement function is discussed, and by comparing with the finite element method, the reliability of the crack model is also verified. Meanwhile, the dynamic characteristics of the blade are studied with the changing of the excitation amplitude and frequency under different crack depth. Fortunately, the detailed dynamic evolutions of the blade and the effects of the crack depth on that are gotten. More importantly, these results can guide the operation of the hydropower station and provide a new method for the identification of the blade crack.

中文翻译：

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裂纹故障灯泡涡轮叶片的建模与动力学分析

摘要 在实际水电工程中，叶片裂纹故障会影响灯泡涡轮的效率和可靠性。为探索这一问题，本文主要研究裂纹故障对不同外部激励下叶片动态特性的影响。首先，创新性地提出裂纹叶片位移函数为多项式容许函数与反映裂纹特征的补充容许函数之和。然后，利用该位移函数，可以通过 Ritz 方法计算裂纹叶片的固有频率和模态函数。此外，基于导出的模态函数，还可以得到裂纹叶片的动力学微分方程。最后，讨论了位移函数的截断敏感性，并通过与有限元方法的比较，验证了裂纹模型的可靠性。同时，研究了叶片在不同裂纹深度下随激励幅度和频率变化的动态特性。幸运的是，获得了叶片的详细动态演变以及裂纹深度对其的影响。更重要的是，这些结果可以指导水电站的运行，为叶片裂纹的识别提供一种新的方法。幸运的是，获得了叶片的详细动态演变以及裂纹深度对其的影响。更重要的是，这些结果可以指导水电站的运行，为叶片裂纹的识别提供一种新的方法。幸运的是，获得了叶片的详细动态演变以及裂纹深度对其的影响。更重要的是，这些结果可以指导水电站的运行，为叶片裂纹的识别提供一种新的方法。