基于频响函数Neumann级数展开的有限元模型修正

Finite element model updating based on Neumann series expansion of the frequency response function

针对有限元模型修正中测试自由度不完备、求解不适定的问题,提出了一种基于频响函数Neumann级数展开的模型修正方法。首先,利用测试和有限元分析模态数据构造完整的实测频响函数。然后,根据Neumann级数展开式建立实测频响函数与有限元模型频响函数之间的关系式,以此构建模型修正目标函数。最后,采用改进鲸鱼优化算法求解目标函数获取修正结果。通过平面桁架数值算例表明,该方法具有较强的噪声鲁棒性,模型修正精度较好,15%噪声时修正后的平均相对误差不超过1%。利用4层剪力框架结构测试算例进一步验证所提方法,结果表明,修正后的模型能反映结构真实状况。

To solve the problem of incomplete measurement and ill-posed in finite element model updating,a model updating method based on the Neumann series expansion of frequency response function(FRF)is proposed.First,the complete test FRF is calculated by modal data from test and finite element analysis.Then,equations between test FRF and analysis FRF are established according to Neumann series.In this way,the objective function of model updating is formulated.Finally,the modified whale optimization algorithm is applied to obtain the updating results.Numerical examples of a plane truss show that the proposed method is robust to noise and has good precision.With 15%noise,the average relative error after model updating is less than 1%.The method is further validated experimentally with the 4-story shear frame structure.Results show that the updated model can reflect the true status of the structure.