含裂纹梁参数的谐响应识别

摘要

A method of crack identification is presented based on amplitude changing after analyzing the dynamic characteristics of cracked beams under harmonic excitation.Firstly,a breathing crack model was introduced to establish a 2-D finite element model of cantilever beam with a crack.It is pointed out that the amplitude is always a significant signal under any excitation and can be used to describe the dynamic characteristics of cracked beams.Secondly,it was found that the amplitudes change differently with crack parameters when the exciting frequency is a quarter of first-order and second-order nature frequency of beams with no cracks.So the amplitude is proposed to detect the crack parameters in beams.Then,the amplitude surface is plotted by adopting surface fitting technology.Through identification of a cracked beam with unknown parameters,the method is proved to be effective.Finally,considering that the nature frequency of a beam with no cracks is calculated inaccurately,the robustness of this method is analyzed. The result shows that this method can detect the crack parameters even though the max error is 10%.%主要研究含裂纹梁在简谐激励作用下的动力特性，提出一种依据幅值变化对裂纹参数进行识别的新方法。首先，在振动过程中考虑裂纹的呼吸特性，以悬臂梁为例建立含裂纹梁的二维有限元模型，指出在一般激励频率下，其对应的幅值均是明显信号，可用来描述裂纹梁的动力特性。其次，当激励频率分别取无裂纹梁一阶频率的1/4和二阶频率的1/4时，幅值随裂纹参数的变化明显不同，可依据响应幅值的变化对裂纹参数进行识别。然后，利用曲面拟合技术绘出幅值变化曲面，对未知参数的裂纹进行识别，验证了该方法的有效性，并归纳出利用幅值变化对任意裂纹参数进行识别的基本步骤。最后，针对无裂纹梁频率计算可能存在误差的情况，分析识别方法的鲁棒性，结果显示即使最大误差为10%，该方法也能对裂纹参数进行准确识别。