基于类柔度差曲率和频率摄动的结构损伤识别

Structural Damage Identification Based on Analogous Flexibility Difference Curvature and Perturbation of Frequency

摘要:

为提高梁式结构损伤诊断的效率，提出一种基于类柔度差曲率和频率摄动的结构损伤识别方法。首先根据结构振动理论，研究广义柔度矩阵计算公式；再利用模态柔度对结构损伤灵敏性高的优点，改进基于柔度差曲率的损伤定位指标，定义类柔度差曲率LCFC损伤指标，并初步识别损伤；最后基于矩阵摄动进行结构损伤识别结果确认。考虑多种损伤工况，对一简支梁结构进行损伤识别数值模拟验证。结果表明：仅使用一阶模态，建立的类柔度差曲率LCFC指标对梁式结构损伤定位具有良好的诊断效果，且计算工作量小；对于含边界损伤单元的多损伤工况，当损伤程度大于10%时，LCFC指标识别有效；当损伤程度不大于25%时，各工况二阶摄动识别结果精度较高，相对误差较一阶摄动结果明显降低，证明了该方法的实用性、有效性和精确性。

Abstract:

To improve the efficiency of damage diagnosis of beam structures, a structural damage identification method, based on the analogous flexibility difference curvature and frequency perturbation was established. First, according to the theory of structural vibration, the calculation formula of generalized flexibility matrix was studied. Utilizing the high sensitivity of modal flexibility to structural damage, the damage location index, based on flexibility difference curvature, was improved, and the damage index of LCFC (the difference of likeness curvature of flexibility coefficient) was defined and used to preliminarily identify damage. Identification result of structural damage was confirmed based on matrix perturbation. Considering various damage conditions, damage identification of the simply supported beam structure was verified by numerical simulation. Results showed that the LCFC index has a good diagnostic effect on the damage location of beam structures using only the first mode. Calculation workload of the index was small. For multi-damage cases with boundary damage elements, the LCFC index was effective when the damage degree was >10%. When the damage degree was < 25%, accuracy of the second-order perturbation identification results was high and the relative error was significantly lower than that of the first-order perturbation identification results, which proved the practicability, effectiveness, and accuracy of the method.