A Modified Iteration Method to Solve the Frequency Response Function of Structures with Interval Parameters

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (13) : 20-25.

FAN Zhiruo1, 2, JIANG Dong1, 2, 3, DONG Eliang1, 2, FEI Qingguo1, 2

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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;

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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[J]. Journal of Vibration and Shock, 2016, 35(13): 20-25

References

[1] 苏静波, 邵国建. 基于区间分析的工程结构不确定性研究现状与展望[J]. 力学进展, 2005, 35(3):338-344.
Su J. B, Shao G. J. Current research and prospects on interval analysis in engineering structure uncertainty analysis [J]. Advances in Mechanics, 2005, 35(3): 338-344.
[2] 邱志平, 王靖. 不确定参数结构特征值问题的概率统计方法和区间分析方法的比较[J]. 航空学报, 2007, 28(3):590-592.
Qiu Z. P, Wang J. Comparison of probabilistic Statistical method and interval analysis method for Eigenvalue problem of structure system with uncertain parameters [J]. ACTA AERONAUTICA ET ASTRONAUTICA SINICA-SERIES A AND B-, 2007, 28(3): 590.
[3] Metropolis N, Ulam S. The monte carlo method [J]. Journal of the American statistical association, 1949, 44(247): 335-341.
[4] Moore R. E, Kearfott R. B, Cloud M. J. Introduction to interval analysis [M]. Society for Industrial and Applied Mathematics, Philadelphia, 2009.
[5] Moens D, Hanss M. Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances [J]. Finite Elements in Analysis and Design, 2011, 47(1): 4-16.
[6] Ben-Haim Y, Elishakoff I. Convex models of uncertainty in applied mechanics [M]. Elsevier, 2013.
[7] Chen S. H, Qiu Z. P, Song D. A new method for computing the upper and lower bounds on frequencies of structures with interval parameters [J]. Mechanics research communications, 1994, 21(6): 583-592.
[8] 邱志平, 陈塑寰, 刘中生. 区间参数结构振动问题的矩阵摄动法[J]. 应用数学和力学, 1994(6): 519-527.
Qiu Z. P, Chen S. H, Liu Z. S. Matrix perturbation method of structure vibration problems with interval parameters [J]. Applied Mathematics and Mechanics, 1994(6): 519-527.
[9] 李金平, 陈建军, 朱增青等. 结构区间有限元方程组的一种解法[J]. 工程力学, 2010, 27(4): 79-83.
Li J. P, Chen J. J, Zhu Z. Q, etc. A method for solving the structural interval finite element equations [J]. Engineering Mechanics, 2010, 27(4): 79-83.
[10] 苏静波, 邵国建, 刘宁. 基于单元的子区间摄动有限元方法研究[J]. 计算力学学报, 2007, 24(4): 524-528.
Su J. B, Shao G. J, Liu N. Static sub-interval perturbed finite element method based on the elements [J]. Chinese Journal of Computational Mechanics, 2007, 24(4): 524-528.
[11] Muhanna R. L, Zhang H, Mullen R. L. Interval finite elements as a basis for generalized models of uncertainty in engineering mechanics [J]. Reliable Computing, 2007, 13(2): 173-194.
[12] Moens D, Vandepitte D. An interval finite element approach for the calculation of envelope frequency response functions [J]. International Journal for Numerical Methods in Engineering, 2004, 61(14): 2480-2507.
[13] Dessombz O, Thouverez F, Laîné J. P, et al. Analysis of mechanical systems using interval computations applied to finite element methods [J]. Journal of Sound and Vibration, 2001, 239(5): 949-968.
[14] Rump S. M. On the solution of interval linear systems [J]. Computing, 1992, 47(3-4): 337-353.
[15] 梁震涛, 陈建军, 王小兵. 不确定性结构区间分析的改进MonteCarlo方法[J]. 系统仿真学报, 2007, 19(6):1220-1223.
Liang Z.T, Chen J. J, Wang X. B. Improved Monte Carlo method for interval analysis of uncertain structures [J]. Journal of System Simulation, 2007, 19(6): 1220-1223.