改进的区间参数结构频响函数迭代解法

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摘要针对区间不确定性系统频响函数求解提出了一种改进的迭代方法。采用区间分析方法描述不确定性结构参数，将频响函数求解转化为区间线性方程组形式，使用定点迭代方法，构造迭代格式；为了解决迭代方法中出现的收敛性问题，结合子区间概念提出改进的迭代方法，计算结构频响函数的区间。以弹簧-质量系统为仿真算例，研究了子区间数目对计算结果的影响。最后，将方法应用于文献中的工程结构，对比研究表明：该方法适用于全频段频响函数分析、具有较高的精度和效率。

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	范芷若1
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	姜东1
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	董萼良1
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	费庆国1
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关键词 ：不确定性, 区间分析, 区间线性方程, 子区间, 频响函数, 中图分类号：TB122

Abstract：A modified method for solving frequency response function of a structure with uncertain parameters is presented. Interval parameters are adopted to represent structural uncertain parameters. The equation to solve frequency response function is transformed to a liner interval equation. The iteration matrix is obtained by using fixed point theorem. Due to the convergence problem in iteration, sub–interval is introduced and a modified iteration method is proposed to get the upper and lower bounds of frequency response function. The accuracy of solution is improved and the convergence problem is solved after modification. A spring-mass system is adopted in simulation study to explore the influence of numbers of sub-interval. At last, a comparative study is conducted using a structure in reference. The results show that the proposed method is suitable for full band frequency response analysis with good accuracy and computation efficiency.

Key words： Uncertainty Interval analysis Liner interval equation Sub-interval Frequency response function;

收稿日期: 2015-04-27 出版日期: 2016-06-25

引用本文:

范芷若1, 2，姜东1, 2, 3，董萼良1, 2，费庆国1, 2. 改进的区间参数结构频响函数迭代解法[J]. 振动与冲击, 2016, 35(13): 20-25.
FAN Zhiruo1, 2, JIANG Dong1, 2, 3, DONG Eliang1, 2, FEI Qingguo1, 2. A Modified Iteration Method to Solve the Frequency Response Function of Structures with Interval Parameters. JOURNAL OF VIBRATION AND SHOCK, 2016, 35(13): 20-25.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2016/V35/I13/20

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