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复模态正交性理论的异常现象及对策分析

张淼 于澜 鞠伟

张淼, 于澜, 鞠伟. 复模态正交性理论的异常现象及对策分析[J]. 应用数学和力学, 2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002
引用本文: 张淼, 于澜, 鞠伟. 复模态正交性理论的异常现象及对策分析[J]. 应用数学和力学, 2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002
ZHANG Miao, YU Lan>, JU Wei. An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002
Citation: ZHANG Miao, YU Lan>, JU Wei. An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It[J]. Applied Mathematics and Mechanics, 2014, 35(10): 1081-1091. doi: 10.3879/j.issn.1000-0887.2014.10.002

复模态正交性理论的异常现象及对策分析

doi: 10.3879/j.issn.1000-0887.2014.10.002
基金项目: 吉林省自然科学基金(201215115)
详细信息
    作者简介:

    张淼(1972—),男,长春人,副教授,博士(通讯作者. E-mail: zm7209@163.com).

  • 中图分类号: O321;TB122

An Unusual Phenomenon in the Complex Mode Orthogonality Theory and the Strategy Against It

  • 摘要: 利用复模态正交性理论的数值实验发现并提出了标号现象.首先根据复模态理论在两种状态空间格式下,对不同振动系统的状态向量解耦功能进行分析,其次提出了对称及非对称重频系统的状态向量正交性的相关结论并进行了数值验证;继而发现并提出了标号现象,并指出了克服标号现象的方法;最后以工程应用中的一个常见的灵敏度分析问题为例,用数值算例的结果说明了忽略标号现象可能存在的风险.
  • [1] 张淼, 于澜, 鞠伟. 基于松弛技术的重频密频结构模态灵敏度分析[J]. 合肥工业大学学报(自然科学版), 2012,35(12): 1605-1609.(ZHANG Miao, YU Lan, JU Wei. Modes sensitivity analysis for multiple frequencies and closely spaced modes structure based on relaxation technique[J].Journal of Hefei University of Technology(Natural Sciences),2012,35(12): 1605-1609.(in Chinese))
    [2] 张淼, 于澜, 鞠伟. 亏损振系广义状态向量灵敏度的移频算法[J]. 计算力学学报, 2013,30(6): 872-878.(ZHANG Miao, YU Lan, JU Wei. Moving-frequency algorithm of generalized eigenvector sensitivity for defective dynamic system[J].Chinese Journal of Computational Mechanics,2013,30(6): 872-878.(in Chinese))
    [3] 盛严, 龚靖, 杨正光. 主动杆系结构的模态性质分析[J]. 噪声与振动控制, 2010,30(5): 6-9, 24.(SHENG Yan, GONG Jing, YANG Zheng-guang. Modal analysis of active framed structure[J].Noise and Vibration Control,2010,30(5): 6-9, 24.(in Chinese))
    [4] 解惠青, 戴华. 阻尼系统重特征对导数的计算[J]. 应用数学和力学, 2007,28(6): 749-756.(XIE Hui-qing, DAI Hua. Derivatives of repeated eigenvalues and corresponding eigenvectors of damped systems[J].Applied Mathematics and Mechanics,2007,28(6): 749-756.(in Chinese))
    [5] 夏品奇, James M W B. 斜拉桥有限元建模与模型修正[J]. 振动工程学报, 2003,16(2): 219-223.(XIA Pin-qi, James M W B. Finite element modeling and model updating of a cable-stayed bridge[J].Journal of Vibration Engineering,2003,16(2): 219-223.(in Chinese))
    [6] Sondipon A. Rates of change of eigenvalues and eigenvectors in damped dynamic system[J].AIAA Journal,1999,39(11): 1452-1458.
    [7] Sondipon A, Friswell M I. Eigenderivative analysis of asymmetric non-conservative systems [J].International Journal for Numerical Methods in Engineering,2001,51(6): 709-733.
    [8] 许鑫, 史治宇. 用于时变系统参数识别的状态空间小波方法[J]. 工程力学, 2011,28(3): 23-28.(XU Xin, SHI Zhi-yu. Parameter identification for time-varying system using state space and wavelet method[J].Engineering Mechanics,2011,28(3): 23-28.(in Chinese))
    [9] 于澜, 张淼, 鞠伟, 谷涛. 非保守系统复模态的规范正交性及其应用[J]. 华南师范大学学报(自然科学版), 2013,45(4): 13-17.(YU Lan, ZHANG Miao, JU Wei, GU Tao. The orthogonality and normalization relationships with its application of complex modes for non-conservative system[J].Journal of South China Normal University (Natural Sciences Edition),2013,45(4): 13-17.(in Chinese))
    [10] 李德葆, 陆秋海. 实验模态分析及其应用[M]. 北京: 科学出版社, 2001.(LI De-bao, LU Qiu-hai.Experimental Mode Analysis and Application[M]. Beijing: Science Press, 2001.(in Chinese))
    [11] Greco A, Santini A. Comparative study on dynamic analysis of non-classically damped linear system[J].Structural Engineering and Mechanics,2002,14(6): 679-698.
    [12] 沈继红, 胡波, 王侃, 金鑫. 二阶振动系统的解耦条件及算法研究[J]. 振动与冲击, 2012,31(18): 89-92, 156.(SHEN Ji-hong, HU Bo, WANG Kan, JIN Xin. Decouplin coupling and algorithm of a quadratic system[J].Journal of Vibration and Shock,2012,31(18): 89-92, 156.(in Chinese))
    [13] Ward H, Stefan L, Paul S.Modal Analysis Theory and Testing[M]. Brussel, Belgium: Katholieke Universiteit Levven, 1997.
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出版历程
  • 收稿日期:  2014-04-18
  • 刊出日期:  2014-10-15

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