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根据矩阵摄动理论,将结构的质量矩阵和刚度矩阵表示为单元损伤参数的函数,提出了根据频率和振型摄动进行结构损伤识别的方法。首先根据结构损伤前后振型变化建立损伤初定方程和损伤确定方程,利用振型摄动求解单元损伤参数,当两次求解得到的同一单元损伤程度基本一致时,可判定该单元损伤;再将损伤识别结果代入基于频率变化的损伤校核方程,用于检验识别结果的准确性。该方法建立的损伤识别方程为超静定方程,可以保证识别结果的唯一性,避免出现“伪损伤”现象。数值算例表明,即使结构出现损伤程度较小的多个单元损伤,只需测试其一阶振型,也可识别。此外,当结构损伤程度较小时,只需采用一阶摄动方程;当结构损伤程度较大时,可采用二阶摄动方程,以提高识别结果的精度。
According to the matrix perturbation theory, the mass matrix and stiffness matrix of the structure are expressed as a function of the unit damage parameters, and a method of structural damage identification based on frequency and mode perturbation is proposed. Firstly, the initial damage equation and the damage determination equation are established according to the change of the vibration modes before and after the structural damage, and the damage parameters of the element are solved by using the mode perturbation. When the degree of damage of the same element obtained by the two solutions is basically the same, the damage of the element can be judged. The damage identification results are substituted into the damage check equation based on the change of frequency to check the accuracy of the identification result. The damage identification equation established by the method is an indeterminate equation, which can ensure the uniqueness of the identification result and avoid the phenomenon of “pseudo-damage”. The numerical examples show that even if the structure has more damage than the other one, only the first mode of vibration can be tested and it can be identified. In addition, the first-order perturbation equation is only used when the degree of structural damage is small, and the second-order perturbation equation can be adopted when the structural damage is large, so as to improve the accuracy of the recognition result.