Free and fixed plate blade root states were simulated with finite element analysis to reveal the crack effect on the natural vibration frequency of the blade. Natural vibration frequencies are obtained for blades with different crack locations and lengths. The crack is found to reduce the blade stiffness and to affect its natural vibration frequency. The longer the crack, the greater the change of the stiffness, and the more the natural vibration frequency decreases. In the free state, the effect of the cracks of the same length on the natural vibration frequency is basically identical when it lies between the two nodal lines of first-order bending vibrations. The crack effect at a height of one-half the blade in the free state on natural frequencies is very close to that of the cracks of the same length at a height of one-eighth the blade in the fixed state. Practical guidelines for the detection of fracture cracks are given and the crack length and location were evaluated by frequency variations.

中文翻译：

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裂纹几何形状对平板叶片固有振动频率影响的模拟

通过有限元分析模拟了自由和固定板叶片的根部状态，以揭示裂纹对叶片固有振动频率的影响。对于具有不同裂纹位置和长度的叶片，可获得自然振动频率。发现裂纹会降低叶片的刚度并影响其固有振动频率。裂纹越长，刚度的变化越大，自然振动频率降低的越多。在自由状态下，当相同长度的裂纹位于一阶弯曲振动的两个节点线之间时，其对固有振动频率的影响基本相同。在自然状态下，在自由状态下叶片高度的一半处的裂纹效果与在固定状态下，高度叶片高度的八分之一处的相同长度的裂纹效果非常接近。给出了检测裂缝的实用指南，并通过频率变化评估了裂缝的长度和位置。