基于裂纹附加模态Timoshenko梁的裂纹损伤识别

将梁中横向裂纹等效为无质量扭转弹簧,并忽略其对梁剪切变形的影响,得到的具有任意裂纹数目Timoshenko梁自振模态的统一显示解析表达式.将裂纹梁的自振模态分为基本模态和裂纹附加模态,利用最小二乘拟合,建立了利用裂纹附加模态函数的梁裂纹损伤识别方法.通过数值模拟开展了简支单裂纹梁以及悬臂和固支双裂纹梁等的裂纹损伤识别,考察了测量误差对损伤识别的影响,数值结果表明本文所提出的裂纹损伤识别方法对裂纹位置的识别精度高于对裂纹损伤程度的识别精度;随着测量误差的增加,裂纹位置及裂纹损伤程度的识别误差增加,但仍在可接受的范围内,故该裂纹损伤识别方法在实际工程中具有一定的应用价值.

Crack Damage Identification of Timoshenko Beam Based on the Additional Vibration Mode Induced by Crack

Regarding a transverse crack in a beam as a massless rotational spring and neglecting its influence on the shear deformation of beam, the unified explicit analytical expression of the vibration mode of Timoshenko beam with arbitrary number of cracks is obtained. The vibration modes of a cracked beam are then divided into the basic mode and the crack-induced additional mode, and a damage identification method of beam crack is established based on the crack-induced additional mode function through the least square fitting. Damage identifications of cracks of a simply-supported beam with single crack, cantilever and clamped-clamped beams with double cracks are carried out numerically, and the influence of measurement noise on the identification accuracy is examined. The numerical results show that, using the crack damage identification method presented in present paper, the identification accuracy of the crack position is higher than that of the crack damage degree. The identification errors of the positions and the damage degrees of the cracks increase with the increase of measurement errors, but are in acceptable range. Therefore, the proposed crack damage identification method is applicable for practical engineering.