含双裂纹圆截面悬臂梁的损伤识别研究

裂纹的萌生和扩展直接影响构件的振动响应，对构件的安全可靠性具有重要影响．本文以圆截面悬臂梁为对象，结合转角模态振型和模态频率等高线，研究了一种双裂纹识别技术．首先，基于应力强度因子和卡氏定理推导了无裂纹梁单元和含裂纹梁单元的刚度矩阵；在此基础上，建立了含裂纹圆截面悬臂梁的有限元动力学方程；然后，结合裂纹对梁转角模态振型和模态频率的影响，提出了双裂纹识别策略．最后，通过算例讨论了双裂纹识别策略的可行性．结果表明，圆截面悬臂梁的模态转角在裂纹位置出现突变，裂纹深度越大转角突变值越大；将识别出的裂纹位置作为已知参数，通过模态频率等高线法，可以准确地识别出双裂纹的深度．

Study on Damage Identification of a Cantilever Beam of Circular Cross Section with Double Cracks

Crack initiation and propagation can affect the vibration response of a component directly, which is very important for the safety and reliability of the components. In this article, a cantilever beam of circular cross section is taken as the study object, and an identification method for double cracks is proposed using the angular modal shape and the modal frequency contours. At first, the stiffness matrix of the uncracked beam element and the cracked beam element were derived using the stress intensity factor and the Castigliano theory. Thereafter, the finite element dynamic model of a cracked cantilever beam with circular cross section was set up. Subsequently, considering the effects of the cracks on the angular modal shape and the modal frequencies, a method for identifying the double cracks was proposed. At the end, case studies were carried out to verify the feasibility of the identification method for double cracks. Results indicate that the modal angle of a cantilever beam with circular cross section changes abruptly at the crack position. The change increases with the increase of crack depth. Using the identified crack position as a given parameter, the depth of the double cracks can be identified by the modal frequency contour method.