悬臂梁中开闭裂纹的损伤识别

利用裂纹诱导弦挠度函数，建立了悬臂Euler-Bernoulli 中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法．为此，首先将梁中开闭裂纹等效为单向扭转弹簧，给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度，并得到悬臂Euler-Bernoulli 开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数，证明了裂纹诱导弦挠度的分段线性函数．其次，基于单向扭转弹簧的性质，建立了通过多步加载进行梁中开闭裂纹参数及其上下侧属性的识别方法．最后，通过数值算例验证了本文所建立的开闭裂纹损伤识别方法的适用性和可靠性，考察了裂纹分布位置、深度和初始张开角以及裂纹识别区间和挠度测量误差等参数对识别结果的影响，结果表明：当裂纹处于张开状态时，裂纹处裂纹诱导弦挠度斜率改变量随着施加荷载的增加而增加；当裂纹闭合时，其裂纹诱导弦挠度斜率改变量将保持为常量；裂纹损伤参数的识别误差随测量误差的增加而增加，但整体识别结果具有较高的精度，较好的鲁棒性．

Damage Identification of Switching Crack of Cantilever Beam

An identification method of damage parameters of location, depth and initial open angle of switching crack in cantilever Euler-Bernoulli beam was established. Frist, regarding the switching crack in the beam as an equivalent unilateral internal rotational spring, the equivalent flexural rigidity of the cracked beam with effect of crack gap was presented, and a general explicit closed-form solution of the bending deflection and its crack-induced chord-wise deflection of the cantilever Euler-Bernoulli beam with switching cracks was obtained. And the piecewise linearity of the crack-induced chord-wise deflection was proved. Then, based on the property of unilateral internal rotational spring, an identification method of parameters and top-bottom attribution of the switching crack in the beam by multi-step loading was proposed. Finally, the validity and reliability of the proposed damage identification method of switching crack were demonstrated by numerical experiments, and the influences of location, depth and initial open angle of the switching crack, the crack identification interval and the deflection measurement error, etc., on identification results were examined. It is revealed that the slope increment of the crack-induced chord-wise deflection at the crack location increases with the increase of loading when the crack is at open state, while the slope increment of the crack-induced chord-wise deflection at the crack location keeps constant when the crack is at closed state. Furthermore, identification errors of the crack damage parameters increase with the increase of the deflection measurement errors, but the identification results generally have higher precision and better robustness.