基于模态参数的梁结构多裂纹定位与程度识别

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摘要针对梁结构多裂纹诊断的问题，基于梁结构的固有频率，提出了一种灵敏度方阵法与单元细分法相结合的多裂纹识别方法。首先，让选用的结构固有频率阶数与梁划分的单元个数相等，基于梁的各阶振型函数计算梁的灵敏度方阵；其次，测量的固有频率，求解灵敏度方阵方程，确定含裂纹单元，并结合单元细分法缩小裂纹所在区域；再次，针对多裂纹梁，基于归零逆求法，依次求得各裂纹单独存在时梁的固有频率参数，将多裂纹诊断问题转化为多个不相关的单裂纹诊断问题；最后，根据梁结构单裂纹定位与程度识别方法，在单元内进一步定位裂纹并识别裂纹程度，最终实现多裂纹的诊断。进行了数值仿真分析及试验，该多裂纹诊断方法精度较高，验证了其有效性，能为实际工程应用提供理论依据。

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	郭帅平1
	吴琪强1
	李学军1
	2
	王钢1

关键词 ：梁结构, 固有频率, 多裂纹诊断, 灵敏度方阵, 归零逆求法

Abstract：Aiming at multi-crack diagnosis problems of beam structure, based on natural frequencies of beam structure, a multi-crack diagnosis method to combine the sensitivity square matrix with the element subdivision was proposed.Firstly, natural frequency orders of a selected beam structure were equal to the number of elements divided in the beam, and the sensitivity square matrix of the beam was calculated based on the beam’s various modal shapes.Secondly, measured natural frequencies of the beam were used to solve the sensitivity square matrix equation, and determine cracked elements.The element subdivision method was employed to reduce crack area.Thirdly, aiming at the multi-crack beam, based on the return to zero inverse method, the beam’s natural frequency parameters were solved in turn when each crack exists alone.The multi-crack diagnosis problem was converted into multiple uncorrelated single-crack diagnosis problems.Finally, according to the beam’s single crack location and degree recognition method, within an element, cracks were further located and their degrees were recognized to realize multi-crack diagnosis.Numerical simulation and tests were performed.Results showed that the proposed beam multi-crack diagnosis method has higher accuracy; its effectiveness is verified; it can provide a theoretical basis for practical engineering application.

Key words： beam structure natural frequency multi-crack diagnosis sensitivity square matrix return to zero inverse method

收稿日期: 2020-02-25 出版日期: 2020-11-28

引用本文:

郭帅平1，吴琪强1，李学军1,2，王钢1. 基于模态参数的梁结构多裂纹定位与程度识别[J]. 振动与冲击, 2020, 39(23): 271-279.
GUO Shuaiping1, WU Qiqiang1, LI Xuejun1,2, WANG Gang1. Multi-crack location and degree identification of beam structure based on modal parameters. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(23): 271-279.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I23/271

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