摘要
将梁中横向开裂纹等效为内部扭转弹簧,利用广义Delta函数和Heaviside函数,给出了具有任意条裂纹Eu-ler-Bernoulli梁振动模态的统一显式解析表达式.在此基础上,引入裂纹附加模态的概念,并根据裂纹附加模态函数的构造特征,利用最小二乘拟合,建立了一种新的裂纹损伤参数识别方法.该方法计算简单,且仅需较少的测量点及测量点处某一模态的测量数据即可实现裂纹位置及深度的识别.最后,通过两个数值算例验证了裂纹损伤参数识别方法的适用性和可靠性,并考察了测量噪声对损伤识别的影响,结果表明裂纹位置识别精度高于裂纹等效弹簧刚度识别精度;前面裂纹识别结果影响后续裂纹的识别结果;随着测量噪声的增加,裂纹位置及裂纹等效弹簧刚度的识别误差增加,但仍在可接受的范围内,故该裂纹损伤识别方法在工程实际中具有一定的适用性.
Regarding the transverse open crack in a beam as an equivalent internal rotational spring,a unified explicit expression of the vibration mode of an Euler-Bernoulli beam with arbitrary number of cracks is obtained with the generalized Delta and Heaviside functions.On this basis,the concept of crack-induced additional vibration mode is proposed,and a novel method to identify the crack damage parameters is established with the constructive feature of the crack-induced additional vibration mode by using the least square fitting.The proposed method has the advantage of simple calculation and can identify the locations and equivalent rotational spring rigidities of the cracks using less mode measurement data.Finally,the validity and reliability of the proposed method for crack-damage identification are validated by two numerical examples,and the influence of the measurement noise on the identification results is examined.It is revealed that the identification precisions of the crack locations are higher than those of equivalent rotational spring rigidities of the cracks,and the identification result of present cracks has influence on the identification result of later ones.The identification errors of the crack location and the rigidity of the crack equivalent rotational spring increase with the increase of the measurement errors,but these errors are acceptable.Therefore,the proposed crack damage identification method can be applied in practical engineering.
作者
杨骁
王天宇
YANG Xiao;WANG Tian-yu(Department of Civil Engineering,Shanghai University,Shanghai 200072,China;School of Civil Engineering,Southeast University,Nanjing 210096,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2019年第3期480-489,共10页
Journal of Vibration Engineering
关键词
裂纹梁
裂纹损伤识别
等效扭转弹簧模型
裂纹附加模态
最小二乘拟合
cracked beam
crack damage identification
equivalent rotational spring model
crack-induced additional mode
least square fitting
