基于固有频率向量的模型修正方法

A Better Method Based on Natural Frequency Vector for Updating Finite Element Model

在固有频率向量概念的基础上,引入了表示模型修正前后2个结构的固有频率向量之间的相关程度的固有频率向量置信准则,提出了一种基于固有频率向量的模型修正方法。在一个8层空间剪切框架模型上,对文中提出的模型修正方法进行了有效性验证,并与传统的基于固有频率灵敏性分析的模型修正方法进行了比较。结果表明,该方法只需用到结构的固有频率信息,且使用很少的迭代步数就可以得到较满意的修正结果。

In finite element models, there always exist some uncertainty parameters which need to be modified so as to make calculated natural frequencies closer to experimentally measured ones. We introduce natural frequency vector （NFV） and natural frequency vector assurance criterion （NFVAC）, and propose our better model updating method. In the full paper, we explain our method in some detail; in this abstract, we just add some pertinent remarks to listing the three topics of explanation. The first topic is. NFV and NFVAC. In this topic, we propose eq. （4） in the full paper for calculating the numerical assurance value defined by NFVAC. The second topic is： the model updating method based on NFV. In this topic, we obtain the optimal orientation and modulus of the NFV. The third topic is. experiments on the model updating method. Its four subtopics are. the establishment of mass and stiffness matrixes （subtopic 3. 1）, the optimization of the orientation of the NFV （subtopic 3.2）, the optimization of its modulus （subtopic 3.3） and the comparison of our method with the traditional iteration updating method based on the natural frequency sensitivity analysis （subtopic 3.4）. In the third topic, we use the shear model of an 8-story frame illustrated in Fig. 1 in the full paper as experimental example to verify the effectiveness of our method. The experimental results, summarized in Tables 2 through 6, show preliminarily that the NFVAC assurance value rises from 0. 999 887 3 to 0. 999 989 6 and that the sum of absolute errors, each of which is the absolute value of the difference between the calculated natural frequency and its corresponding measured one, decreases from 1. 387 Hz to 0. 393 Hz.