不确定边界条件下悬臂梁裂纹参数识别方法研究  

Identification of Crack Parameters in Cantilever Beam Under Uncertain end Conditions

作　　者：王志华[1] 程载斌[2] 马宏伟[3] 

机构地区：[1]太原理工大学,太原030024 [2]中国科学院力学研究所,北京100080 [3]暨南大学,广州510632

出　　处：《应用力学学报》2007年第1期83-87,共5页Chinese Journal of Applied Mechanics

基　　金：山西省自然科学基金资助项目(20041007);山西省自然科学基金资助项目(20041003)

摘　　要：基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的悬臂梁实验来说明本文方法的有效性。实验结果表明:只需梁结构前三阶频率即可识别裂纹位置和深度。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。The local softening effect at the crack location can be simulated by an equivalent spring connecting the two segments of the beam.Similar to the modeling of crack,the non-perfectly rigid clamp is also simulated by a torsional spring of unknown stiffness.Combined with the Bernoulli-Euler theories of beam,the present model is applied to derive the characteristic equation of the cantilever beam under uncertain end conditions.Based on this characteristic equation,the accurate crack identification method is developed to identify the location and the depth of the crack by minimizing the difference between the analytical and experimental frequencies only with the first three natural frequencies of the test.The proposed approach is verified by two cantilever beam experiments under ideal boundary conditions and uncertain end conditions,and the approach presented here is suitable for crack identification in engineering even if small frequency measuring errors exist.

关 键 词：裂纹 参数识别 悬臂梁 

分 类 号：O347.4[理学—固体力学]