基于点谱相关函数的悬臂结构损伤识别

针对悬臂结构，提出基于点谱相关函数的损伤识别柔度法。该方法依据结构动力特征方程和悬臂结构的特点，利用柔度矩阵元素作为过渡，得到了结构模态参数与杆件物理参数之间的对应关系等式，讨论并提出利用结构自由振动信号的winger-ville点谱相关函数平方根值代替结构模态参数的方法，建立了点谱相关函数平方根值与刚度损伤系数的方程，通过求解方程组就能识别出结构单个或多个损伤的位置和程度。该方法物理意义明确，突卸荷载激励容易实现，且只需一次测量，无需损伤前后对比测试，有利于工程应用。最后通过两个数值算例，验证了所提方法的有效性。

Study on Damage Detection of Cantilever Structure Based on Point Spectral Correlation Function

A damage identification method for the cantilever structure was proposed based on point spectral correlation function. According to the characteristics of the cantilever structure and the structural dynamic equation, the relational equation between the modal parameters and the structural member physical parameters was found by the transition of the flexibility matrix elements. Based on the free vibration signal of structure, the square root value of point spectrum correlation function was discussed and used as a replace of structure modal parameter. Then the damage equation of the square root value of point spectrum and the stiffness damage coefficient was established. The location and degree of single or multiple structure damage will be able to identify through solving the damage equation. This method has clear physical meaning and the unload excitation is easy to implement, and it will be helpful for applications without contrast test before and after damage. Finally, the effectiveness of the proposed method was verified through two numerical examples.