| 唐盛华,罗承芳,方志,张学兵,楚加庆.振型归一化对梁结构柔度曲率损伤指标的影响[J].计算力学学报,2020,37(3):340~348 |
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| 振型归一化对梁结构柔度曲率损伤指标的影响 |
| 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：10.7511/jslx20190618002 |
| 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 |
| 基金项目: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（KLDRES002）资助项目. |
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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梁结构柔度曲率类损伤指标的影响，根据梁结构的刚度、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，实现定量分析均匀荷载面曲率结构损伤程度。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 calculated from the mass normalized mode shapes,but these mode shapes are difficult to measure directly,which limits the application of flexibility curvature damage index.In order to analyze the influence of mode shape normalization method on flexibility curvature damage index of beam structures,according to the relationship between stiffness,bending moment and displacement curvature of beam structures,the theoretical relationship expression of displacement curvature and damage severity before and after structural damage under uniform load was established.The structural damage severity 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-normalized normalized mode shapes and the damage severity was derived from the ULSC index.The theory was verified in the simulation example of a three-span continuous beam.The results show that the quantitative index of damage degree is effective.Under different P-norm mode shape normalization methods,the damage severity deviation can be estimated by 2xα.The damage identification result of 2-norm mode shape normalization method is the closest to the mass normalized mode shapes are normalization result.Therefore,when the mass matrix normalized mode shape is not available,2-norm normalized mode shapes can be used instead. |
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