基于裂纹诱导弦挠度的简支外伸梁裂纹损伤识别

基于梁横向开裂纹的线性扭转弹簧模型，给出了具有任意裂纹数目的简支外伸梁弯曲挠度的显式解析解，研究了集中载荷作用下简支外伸梁裂纹诱导弦挠度函数的性质，给出了裂纹位置和裂纹等效扭转弹簧柔度的近似表达式，从而实现了梁横向裂纹位置及裂纹损伤程度的识别．在此基础上，为利用裂纹梁的测量挠度识别裂纹损伤，提出了分段线性函数的最佳拟合法，实现了简支外伸梁裂纹的损伤参数识别．通过数值试验验证了该识别方法的适用性和可靠性，考察了识别结果对梁挠度测量误差和裂纹深度的敏感性，结果表明随着挠度测量误差的增大，裂纹损伤参数识别误差增大，但裂纹损伤识别方法具有较强的鲁棒性，在工程实际中具有一定的应用性．

Crack Damage Identification of Simply-Supported Overhanging Beam Based on Crack-Induced Chord Deflection

Based on linear rotational spring model of the transverse open crack in beam, an explicit analytical solution of the bending deflection of a simply-supported overhanging beam with arbitrary number of cracks was presented. Properties of the crack-induced chord deflection of the simply-supported overhanging beam subjected to a concentrated load were studied, and the approximate expressions of the crack location and the compliance of equivalent rotational spring of the crack were given. Therefore, the crack damage identification of the beam’s transverse crack was achieved. On this basis, in order to identify the crack damage from the measured deflections of the cracked beam, an optimized fitting method of piecewise linear function was presented, and the crack damage parameters identification was achieved. The feasibility and reliability of the proposed method were validated by numerical experiments. The sensitivities of the identification results with respect to the deflection measurement error and the crack depth were examined. It is revealed that, with increase of deflection measurement error, the identification errors of the crack damage parameters increase. Nevertheless, the proposed crack-damage identification method has strong robustness and can be applied in engineering practice.