频响函数残差法在有限元模型修正中的应用

摘要

Dynamic information of actual structures can be reflected by accurate finite element models effectively. In order to reduce the error in structural modeling, it is necessary to update the finite element model. Currently, the updating methods based on modal frequencies, mode shapes and FRF have been used widely. Among them, the method based on FRF has more advantages than the others since it can avoid the error from modal parameters identification and its testing DOF is unlimited. According to the objective function, the method based on FRF can be classified into FRF correlation method and FRF residual-error method. The FRF correlation method is based on the correlation of mode shape and amplitude with parameters sensitivity. However, in comparison with the FRF residual-error method, this method loses the direct correlation between the FRF and design parameters so that the oscillation and divergence phenomena occur in the model updating for some structures. Therefore, with an actual structure as the object, the two methods in the finite element model updating are compared each other; and the effect of the frequency points and frequency range on the model updating based on FRF residual-error method is analyzed. The results show that the residual-error method can lead to a stable convergence and it has high efficiency. Meanwhile, reasonable frequency points and wider frequency range are beneficial to improving the updating efficiency.%准确的有限元模型能够真实有效地反映实际结构的动态信息，为缩小结构建模中的误差极有必要对结构有限元模型进行修正。目前，基于模态频率、振型和频响函数的模型修正方法应用最广。其中基于频响函数的修正方法避免了模态参数识别过程的误差，且不受测试自由度数限制，与模态频率和振型的模型修正方法相比更具有优势。基于频响函数的修正方法按目标可分为频响函数相关性法和频响函数残差法。频响相关性法立足于形状和幅值相关性与参数灵敏度的关系，与频响函数残差法相比，丧失了频响函数与设计参数的直接关联，导致在部分结构模型修正中出现振荡不收敛现象。为此，基于实际测试结构对比研究两种方法在有限元模型修正中的应用，并分析频率点数和频带范围对基于频响函数残差法的模型修正的影响。结果表明频响函数残差法能够稳定收敛且具有高效性；同时，合理的频率点数和较宽频带范围有利于提高频响函数残差法的修正效率。