基于模态频率和有效模态质量的有限元模型修正

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A new finite element model updating method was presented using modal frequency and effective modal mass as residues of objective values. The effective modal mass could not only provide a method for judging the level of significance of a vibration mode in a structural dynamic analysis, but also provide more useful information for model updating. The process of model updating based on sensitivity analysis and the concept of effective modal mass was introduced, mean while the sensitivities of effective modal mass with respect to physical parameters were derived. The simulation results showed that all updated parameters return to the given objective values and the root mean square （RMS） errors for both the modal frequency and the effective modal mass are less than 0.4% even taking 5% Gaussian white noise into account for the estimated modal parameters. The study demonstrated that the finite element modal updating method based on modal frequency and effective modal mass is feasible and effective.提出一种同时使用模态频率和有效模态质量作为目标量的残差进行结构动力学有限元模型修正的新方法。有效模态质量不但可以为结构动力学分析提供一种判断振动模态重要程度的方法，而且能够为有限元模型修正提供更多的信息量。介绍了基于灵敏度分析的模型修正实现过程以及有效模态质量的概念，推导了有效模态质量对设计参数的灵敏度，在此基础上采用仿真算例验证了所提出方法的正确性和有效性。仿真结果显示所有修正参数都回到了设定的目标值，即使当模态频率和有效模态质量等特征量都存在5％的高斯白噪声时，修正后在修正频段内特征量的均方误差都小于0．4％。研究表明，基于模态频率和有效模态质量的结构动力学有限元模型修正是有效可行的。