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振型归一化对梁结构柔度曲率损伤指标的影响
Analysis of the Influence of Mode Shape Normalization on Flexibility Curvature Damage Index of Beam Structure
投稿时间:2019-06-18  修订日期:2019-08-12
DOI:
中文关键词:  损伤识别  振型归一化  柔度矩阵  曲率  范数
英文关键词:damage identification  mode shape normalization  flexibility matrix  curvature  norm  damage degree
基金项目:国家自然科学基金项目(面上项目,重点项目,重大项目)
作者单位E-mail
唐盛华 湘潭大学土木工程与力学学院 tshtangshenghua@163.com 
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中文摘要:
      结构柔度矩阵需由质量矩阵归一化振型获得,而质量矩阵归一化振型难以直接测得,限制了柔度曲率类损伤指标的应用。为分析振型归一化方法对柔度曲率类损伤指标的影响,根据梁结构刚度、弯矩和位移曲率的关系,建立了均布荷载作用下结构损伤前后位移曲率与损伤程度的理论表达式,实现均匀荷载面曲率结构损伤程度定量。提出P-范数振型归一化方法,通过均匀荷载面曲率指标推导了振型质量矩阵归一化系数差xα与损伤程度的关系。以三跨连续梁算例对理论进行了验证,结果表明:损伤程度定量指标效果良好,不同P-范数振型归一化方法下,损伤程度的偏差可由2xα估算;2-范数振型归一化方法的损伤识别结果与质量矩阵振型归一化结果最接近,故当无法获得质量矩阵归一化振型时,可采用2-范数归一化振型代替。
英文摘要:
      The structural flexibility matrix needs to be obtained from the mass matrix normalized mode shape, but it is difficult to directly measure the mass matrix normalized mode shape, which limits the application of flexibility curvature damage index. In order to analyze the influence of mode shape normalization method on damage identification of flexibility curvature damage index. According to the relationship between stiffness, bending moment and displacement curvature of beam structure, the theoretical relationship expression of displacement curvature and damage degree before and after structural damage under uniform load was established. The structural damage degree was quantified by the uniform load surface curvature (ULSC). The P-norm mode shape normalization method was proposed. The relationship between the coefficient difference xα of mass matrix normalized mode shape and the damage degree was derived from the ULSC index. The theory was verified by a three-span continuous beam example. The results show that the quantitative index of damage degree is effective. Under different P-norm mode shape normalization methods, the damage degree deviation can be estimated by 2xα, the damage identification result of 2-norm mode shape normalization method is the closest to the mass matrix mode shape normalization result. Therefore, when the mass matrix normalized mode shape is not available, 2-norm normalized mode shape can be used instead.
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