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研究了基于Timoshenko梁静态挠度识别梁中裂纹位置及损伤程度的计算方法。首先,将梁开闭裂纹等效为单向旋转弹簧,利用Delta函数和Heaviside函数,得到了具有任意开闭裂纹数目梁的等效抗弯刚度,求得了开闭裂纹Timoshenko梁弯曲变形的显式闭合通解,给出了闭合通解待定常数的迭代求解方法。其次,建立了裂纹诱导弦挠度函数,证明了在裂纹处裂纹诱导弦挠度曲线斜率存在突变,为裂纹位置识别提供了理论依据。在此基础上,给出了裂纹等效旋转弹簧刚度的近似计算公式。最后,通过数值试验,将所建立的方法分别应用于裂纹位置及损伤程度已知的简支和固支Timosheoko梁裂纹位置识别和损伤程度计算,结果表明该文建立的裂纹损伤识别方法不仅具有一般的适用性,而且具有较高的精度和可靠性。
The calculation method of crack position and damage degree in beam based on Timoshenko beam static deflection is studied. First, the open-and-open crack is equivalent to a unidirectional torsional spring. By using the Delta function and the Heaviside function, the equivalent bending stiffness of a beam with any number of open and close cracks is obtained, and the explicit deformation of the Timoshenko beam is obtained. The general solution is closed, and the iterative method of solving the pending constant of the general solution is given. Secondly, the crack-induced chord-deflection function is established. It is proved that there is a sudden change in the slope of the curve induced by crack-induced chord deflection at crack location, which provides a theoretical basis for crack location identification. On this basis, the approximate formula of the equivalent stiffness of the cracked spring is given. Finally, the numerical simulation is applied to the crack position identification and damage degree calculation of simply supported and clamped Timosheoko beams with crack location and degree of damage respectively. The results show that the proposed crack damage identification method not only has the general The applicability, but also with high accuracy and reliability.