考虑轴力二阶效应悬臂梁的支承及裂纹参数识别

建立了轴向压力作用下悬臂裂纹梁边界支承和裂纹损伤程度识别方法．首先，将悬臂梁边界非完整支承等效为竖向和扭转弹簧、梁中开裂纹等效为内部扭转弹簧，利用Laplace变换，得到了边界弹性支承、考虑轴向压力二阶效应、具有任意裂纹数目Euler-Bernoulli悬臂梁弯曲挠度的解析解．其次，提出了边界弹性支承弹簧柔度和裂纹等效扭转弹簧柔度的识别方法．最后，通过数值试验，考察了轴向压力，裂纹深度以及测量误差等对识别结果的影响，说明了本文考虑轴向压力二阶效应的悬臂梁边界支承弹簧柔度及裂纹等效扭转弹簧柔度识别方法的适用性和可靠性，结果表明：相比于应变测量误差，挠度测量误差对裂纹损伤程度识别结果影响更加敏感，且轴向压力对裂纹损伤程度识别影响较小，因此，应严格控制挠度的测量误差．同时，边界支承扭转弹簧柔度的识别误差大于其竖向弹簧柔度识别误差．这些结果为实际工程中边界非完整支承悬臂裂纹梁的参数识别提供了指导．

Parameter Identification of Supporting and Crack of Cantilever Beam with Second-Order Effect of Axial Load

An identification method of boundary supporting and crack damage degree of cantilever cracked beam with second- order effect of axial compressive load was established. Frist, regarding the nonholonomic supporting boundary of the cantilever beam as a vertical and rotational spring and the crack in the beam as an equivalent internal rotational spring, respectively, the analytical solution for bending of cantilever Euler-Bernoulli beam with second-order effect of axial compressive load and arbitrary number of cracks was derived by means of Laplace transform. Then, identification method of boundary elastic supporting compliances and crack equivalent internal rotational spring compliances was presented. Finally, the influences of axial compressive load, crack depth and measurement error, etc., on the identification results were examined by numerical experiments, and the validity and reliability of the proposed identification method were demonstrated. It is revealed that, in comparison to the error of strain measurement, the identification result of the crack damage degree is more sensitive to the error of deflection measurement, and there is a little influence of the axial compressive load on the crack damage degree. Thus, the error of deflection measurement should be strictly controlled. Furthermore, identification error of the boundary rotational spring compliance is larger than that of of the boundary vertical spring compliance. All these results can provide guidance for parameter identification of the cantilever cracked beam with nonholonomic supporting boundary in practice.