修正无阻尼结构系统的一种有效迭代法

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 886-900.

修正无阻尼结构系统的一种有效迭代法

袁永新¹, 赵文华², 刘皞³

1. 湖北师范大学数学与统计学院湖北黄石 435002;
2. 湖北师范大学图书馆湖北黄石 435002;
3. 南京航空航天大学理学院南京 210016

收稿日期:2015-12-26 修回日期:2016-06-28 出版日期:2016-10-26 发布日期:2016-10-26
作者简介:袁永新,E-mail:yuanyx_703@163.com
基金资助:
国家自然科学基金（11401305）资助

An Effective Iterative Updating Method for Undamped Structural Systems

Yuan Yongxin¹, Zhao Wenhua², Liu Hao³

1. School of Mathematics and Statistics, Hubei Normal University, Hubei Huangshi, 435002;
2. Library of Hubei Normal University, Hubei Huangshi, 435002;
3. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016

Received:2015-12-26 Revised:2016-06-28 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11401305)

摘要/Abstract

摘要：

结构动力学模型修正就是使得分析结果与实验结果的差最小化的一种程序.该文给出了一种基于不完全测量模态数据同时修正质量矩阵与刚度矩阵的迭代方法.通过此方法，在不计舍入误差的情况下，通过选取特殊的初始矩阵对，经有限步迭代，可得到满足特征方程的最优近似质量矩阵与刚度矩阵，并且保持了初始模型的高阶未测量且未知的特征信息.两个数值例子验证了该文给出的迭代算法是有效的.

关键词: 模型修正, 迭代算法, 部分指定谱信息, 无溢出, 无阻尼振动系统, 最优逼近

Abstract:

Structural dynamics model updating is a procedure to minimize the differences between analytical and experimental results. In this paper, an iterative method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By the method, the optimal approximation mass and stiffness matrices which satisfy the required eigenvalue equation can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrix pair. The large number of unmeasured and unknown eigeninformation of the original model is preserved. Two numerical examples show that the introduced iterative algorithm is quite efficient.

Key words: Model updating, Iterative algorithm, Partially prescribed spectral information, No spill-over, Undamped structural system, Optimal approximation

中图分类号:

O241

袁永新, 赵文华, 刘皞. 修正无阻尼结构系统的一种有效迭代法[J]. 数学物理学报, 2016, 36(5): 886-900.

Yuan Yongxin, Zhao Wenhua, Liu Hao. An Effective Iterative Updating Method for Undamped Structural Systems[J]. Acta mathematica scientia,Series A, 2016, 36(5): 886-900.

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