基于裂纹诱导弦挠度函数的构造特征, 研究了任意边界条件下的 Euler-Bernoulli 梁 中裂纹的静力损伤识别方法. 首先, 将裂纹等效为线性扭转弹簧, 得到了任意边界条件下裂纹 Euler-Bernoulli 梁静力弯曲挠度的解析通解; 然后, 证明了裂纹诱导弦挠度函数为分段三次多 项式函数, 并建立了基于挠度测量的、通过拟合裂纹诱导弦挠度函数识别裂纹位置和裂纹等效 扭转弹簧柔度的数值方法; 最后, 数值验证了所提出的裂纹损伤识别方法的适用性和可靠性, 考察了挠度测量误差、裂纹位置和深度等对损伤识别结果的影响. 结果表明: 裂纹位置的识别 精度高于裂纹等效扭转弹簧柔度的识别精度, 裂纹数量及裂纹识别区间的选取对裂纹损伤识 别结果的影响有限, 所提出识别方法具有较强的鲁棒性.

Based on the constructional characteristics of the crack-induced chord deflection function, the static damage identification method for cracks in Euler-Bernoulli beams with arbitrary boundary conditions is presented. First, with the crack taken as a linear torsional spring, the general analytical solution of the static bending deflection of the cracked Euler-Bernoulli beam with arbitrary boundary conditions was obtained. Second, its crack-induced chord deflection function was proven to be a piecewise cubic polynomial function, and a deflection-based numerical method was developed to identify the crack location and its equivalent torsional spring flexibility by fitting a crack-induced chord deflection function. Finally, the applicability and reliability of the crack damage identification method presented were verified numerically, and the influences of deflection measurement error, crack location, and depth on the damage identification results were examined. The accuracy of identifying the crack location was found to be higher than that of crack equivalent torsional spring flexibility, and the number of cracks and the selection of the crack identification interval have limited influence on the crack damage identification results. The identification method has strong robustness.