摘要
基于模态柔度矩阵曲率范数差构造了一种损伤识别新指标。首先对损伤前后柔度矩阵按列、行分别求两次曲率,再对曲率矩阵的列向量求2-范数差,得到2-范数下各节点的损伤定位指标值。根据梁式结构刚度和位移曲率的负相关关系,推导出准确定量损伤程度的理论表达式,对单损伤和相邻多损伤进行了损伤定量分析。基于串联弹簧原理,提出了等效损伤程度分析模型,建立了测点间梁单元局部损伤与全损伤之间的损伤程度对应关系。采用某三跨连续梁用作仿真算例,结合已有的均匀荷载面曲率差指标,并考虑多种损伤工况,对指标进行对比分析,结果表明该方法仅需低阶模态参数即可进行损伤检测,且具有较好的抗噪声能力。采用对比测点间梁单元局部损伤与全损伤工况基频的方法,验证了所提等效损伤程度计算方法的合理性。
A new damage identification index based on the curvature norm difference of modal flexibility matrix is constructed.Firstly,twice curvature of modal flexibility matrixes before and after the damage is calculated respectively,the curvature is first calculated by columns,and then by rows.After that,2-normdifference of column vector of curvature matrix is computed,and the damage location indicator values of each node are obtained.According to the relationship between displacement curvature and structural stiffness,an explicit calculation formula for damage degree identification is proposed,which quantifies the damage of single damage and adjacent multiple damage.Then,based on the principle of series spring,an equivalent damage degree analysis model is proposed to establish the relationship between the damage degree of local damage and total damage of the beam element between the measuring points.A three-span continuous beam is used to verify the new indicator in various damage cases.Compared to the change in uniform load surface curvature,it shows that the new indicator can effectively identify damage with only a few low order modal parameter sand has a certain anti-noise performance.By comparing the fundamental frequency of the beam under local element damage and total element damage conditions between the measuring points,the method of calculating the equivalent damage degree is verified.
作者
唐盛华
罗承芳
方志
苏彬建
张学兵
楚加庆
Tang Shenghua;Luo Chengfang;Fang Zhi;Su Binjian;Zhang Xuebing;Chu Jiaqing(Key Laboratory of Dynamics and Reliability of Structures,College of Hunan Province,College of Civil Engineering and Mechanics,Xiangtan University,411105,Xiangtan,China;College of Civil Engineering,Hunan University.410082,Changsha,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2020年第3期982-989,I0005,共9页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(51508488)
湖南省自然科学基金(2019JJ50605)
“工程结构动力学与可靠性分析湖南省高等学校重点实验室(湘潭大学)”开放课题资助(KLDRES002)。
关键词
损伤识别
损伤程度
曲率
连续梁
柔度矩阵
范数
damage identification
damage degree
curvature
beam
modal flexibility matrix
norm
