边界非完整约束悬臂裂纹梁的静力参数识别

doi:10.12066/j.issn.1007-2861.1878

摘要/Abstract

摘要：

建立了边界非完整约束悬臂裂纹梁边界支承柔度和裂纹损伤程度的静力参数识别方法. 首先, 将悬臂裂纹梁边界非完整约束等效为竖向和扭转弹簧, 梁中开裂纹等效为内部扭转弹簧, 得到了弹性支承边界悬臂Euler-Bernoulli裂纹梁静力弯曲的显式闭合通解; 其次, 根据弹性支承悬臂裂纹梁的损伤诱导挠度函数和裂纹诱导弦挠度函数是分段线性函数等性质, 给出了边界弹性支承柔度和裂纹损伤程度的计算公式; 最后, 通过数值试验验证了该悬臂裂纹梁边界弹性支承柔度及裂纹损伤程度识别方法的适用性和可靠性, 考察了挠度测量噪声和裂纹深度等对参数识别的影响. 试验结果表明, 随着挠度测量误差的增大, 参数识别误差总体随之增大, 但识别结果仍在可接受的范围内, 因此该方法可用于实际工程中的边界非完整约束悬臂裂纹梁的参数识别.

关键词: 悬臂梁, 边界弹性支承, 裂纹等效扭转弹簧, 广义函数, 诱导挠度, 参数识别

Abstract:

A method of static parameter identification for boundary supporting compliance and the degree of crack damage of cantilever cracked beam with nonholonomic constraint boundary is developed. First, regarding the nonholonomic constraint boundary of the beam as a vertical and rotational spring, and the crack in a beam as an equivalent internal rotational spring, an explicit closed-form solution to static bending of cantilever Euler-Bernoulli cracked beam is derived. According to the properties of piecewise linear functions of damage-induced deflection and crack-induced chord deflection the formulae of boundary elastic supporting compliances and the degree of crack damage are derived. Numerical experiments are performed to show validity and reliability of the proposed method, and influences of factors such as deflection measurement noise and crack depth on the identification results are examined numerically. It is revealed that parameter identification errors increase as a whole with increase of deflection measurement errors. Nonetheless, the results are acceptable. The proposed method is applicable in practice.

Key words: cantilever beam, boundary elastic supporting, crack equivalent rotational spring, generalized function, induced deflection, parameter identification

中图分类号:

TU223
TU317

杨骁, 孟哲, 黄瑾. 边界非完整约束悬臂裂纹梁的静力参数识别[J]. 上海大学学报(自然科学版), 2019, 25(1): 120-131.

YANG Xiao, MENG Zhe, HUANG Jin. Static parameter identification of cantilever cracked beam with nonholonomic constraint boundary[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(1): 120-131.

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