基于波传播和阻抗特性的裂纹梁损伤识别

基于结构振动波传播理论,讨论了在简谐力作用下,裂纹简支梁的弯曲波动解。为了描述由裂纹引起的梁中波传播的不连续特性,引入弯曲弹簧模型来模拟裂纹,并在此基础上提出了利用梁结构驱动点阻抗特性的裂纹损伤识别方法。以一裂纹简支梁为例进行了数值分析,得到了裂纹简支梁的驱动点阻抗特性曲线。从该曲线可以发现,梁的第一阶谐振频率和反谐振频率都随裂纹的出现而减小,并且频率减少量随裂纹尺寸的增大而增加。结合裂纹梁第一阶谐振频率与驱动点位置关系曲线,利用曲线上出现的突变点,准确地识别了梁的损伤状态和裂纹损伤位置。最后,利用已识别的裂纹位置和第一阶固有频率定量地识别了裂纹尺寸。

Beam Crack Identification Based on Wave Propagation and Impedance Method

Based on wave propagation theory,the wave solution of a simply supported beam with a crack is investigated.To characterize the local discontinuity due to the crack,a rotational spring model is proposed to model the crack,on the basis,a method for crack identification is presented in this paper,which makes use of the driving-point mechanical impedance characters of the cracked beam stimulated by harmonic force.Subsequently,the method is verified by a numerical example of a simply supported beam,and some graphs depicting the driving point impedance characters of the simple supported cracked beam are drawn.It is shown that the first resonant frequency and the first anti-resonant frequency decrease synchronously due to the propagation of crack.Combined with the graph correlating the first resonance frequency with driving point location,the method localizes the crack by monitoring a jump in the graph.Finally,the size of the crack is identified by using the identified crack location and the first natural frequency.