损伤悬臂梁固有频率精确测量与分析

Measurement and Analysis of Natural Frequency of Damaged Cantilever Beam

摘要: 本文推导了悬臂梁损伤位置与结构损伤前后固有频率变化的关系，进而可计算悬臂梁损伤位置。为了减小悬臂梁固定端夹紧力波动对测量结果的影响，设计了一套具有较高精度的固有频率测量方法，并对该方法的精确性进行了实验验证，实验证明采用该方法可使固有频率测量值的平均相对误差降至0.7%以下。针对损伤前后悬臂梁的固有频率计算分析与测量，结果表明：通过固有频率变化得到出结构的损伤位置与实际位置基本一致。

Abstract: The relationship between the damage position of cantilever beam and the natural frequency change before and after structural damage is derived. In order to reduce the influence of the clamping force fluctuation of the fixed end of the cantilever beam on the measurement results, a set of natural frequency measurement method with high precision is designed. The accuracy of the method is verified by experiments. It is proved that the average relative error of the measured natural frequencies can be reduced to less than 0.7%. It calculated and analyzed the natural frequency of the cantilever beam before and after the damage. The results show that the damage position of the structure obtained by the natural frequency change is basically consistent with the actual position.