利用附加质量的设计参数型模型修正方法

Design parameter oriented model updating method using additional masses

针对利用附加质量的模型修正方法存在未知修正变量数目过多，修正方程欠定，修改精度无法满足工程应用要求的问题，提出了一种设计参数型修正方法来提高原始方法的修正精度．该方法利用泰勒展开公式，导出质量矩阵和刚度矩阵对设计参数的灵敏度影响矩阵，进而建立以设计参数偏差量为未知数的修正方程．分别用一个长直机翼模型和一个阶梯变截面梁模型为例，进行了该修正算法的验证．两个算例初始引入的局部刚度建模误差为30％-50％，修正后模型的计算误差都小于1％．研究结果表明，本文提出的修正方法大大减少了待求解的未知变量数目，降低了对测试模态数目的要求，提高了算法的修正精度，同时使得修正结果的物理指示意义也更加明确．

As there are too many unknown variables which need to be updated for the model updating method using additional masses, the updating equation conducted by this method is an underdetermined equation, and the updating accuracy cannot meet the requirements of engineering applications. A design parameter oriented model updating method was presented to improve the accuracy of this method. Taylor＇s series of the system matrices expanded with respect to design parameters were adopted, and the sensitivity influence matrices of stiffness and mass were derived, then updating objects were converted to design parameters. A straight wing model and a step section beam were performed as numerical examples to verify the improved method. For the two examples, local stiffness errors in the range of 30% to 50% were introduced into the initial finite element models. The calculation errors obtained by the updated finite element models were less than 1% for both examples. The results showed that the presented method can largely reduce the number of unknown variables, and just limited measured modes were needed, and the updating accuracy was also better than that of the original method and furthermore, the physical indications of updating results were clearer than that of the original method.