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参数振动受迫响应的三角级数解

黄迪山

黄迪山. 参数振动受迫响应的三角级数解[J]. 应用数学和力学, 2013, 34(3): 297-305. doi: 10.3879/j.issn.1000-0887.2013.03.009
引用本文: 黄迪山. 参数振动受迫响应的三角级数解[J]. 应用数学和力学, 2013, 34(3): 297-305. doi: 10.3879/j.issn.1000-0887.2013.03.009
HUANG Di-shan. Trigonometric Series Approach for Forced Parametric Vibration Response[J]. Applied Mathematics and Mechanics, 2013, 34(3): 297-305. doi: 10.3879/j.issn.1000-0887.2013.03.009
Citation: HUANG Di-shan. Trigonometric Series Approach for Forced Parametric Vibration Response[J]. Applied Mathematics and Mechanics, 2013, 34(3): 297-305. doi: 10.3879/j.issn.1000-0887.2013.03.009

参数振动受迫响应的三角级数解

doi: 10.3879/j.issn.1000-0887.2013.03.009
详细信息
    作者简介:

    黄迪山(1957—) ,男, 浙江诸暨人,副教授,博士(E-mail:hdishan@shu.edu.cn)

  • 中图分类号: O242.1;O321

Trigonometric Series Approach for Forced Parametric Vibration Response

  • 摘要: 基于调制反馈方法,对参数周期与激励力周期不相同情况下,研究其参数系统受迫振动响应三角级数解.采用谐波的线性组合形式从数学上表达受迫振动响应解,然后通过运用谐波平衡,将参数振动方程转化成无限阶线性代数方程组,解出其谐波的系数.上述方法的特点在于:1) 用三角级数来表达振动受迫响应,十分便于参数振动的频域分析,剖析受迫响应性质;2) 从解的表达可直接推出组合谐波共振条件; 3) 采用标准的RungeKutta算法得到的相图证实上述方法结果的精确性.研究结果表明:该方法适用于参数振动完整受迫响应解的数学表达与分析.
  • [1] Yakubovitch V A, Starzhinskii V M. Linear Differential Equation With Periodic Coefficients [M].Vols Ⅰand Ⅱ.New York: Wiley, 1975.
    [2] 胡海岩.应用非线性动力学[M].北京: 航空工业出版社, 2000.(HU Haiyan. Application of Nonlinear Dynamic [M].Beijing: Aviation Industry Press, 2000.(in Chinese))
    [3] Gaonkar G H, Simha Prasad D S, Sastry S.On computing Floquet transition matrices of rotorcraft[J]. Journal of the American Helicopter Society , 1981, 26(3): 56-61.
    [4] Sinha S C, WU Der-ho, Juneja V, Joseph P.Analysis of dynamic systems with periodically varying parameters via Chebyshev polynomials[J]. Transaction of the ASME, Journal of Vibration and Acoustics , 1993,115(1): 96-102.
    [5] 丁虎, 胡超荣, 陈立群, 江海燕.轴向变速黏弹性Rayleigh 梁非线性参数振动稳态响应[J].振动与冲击, 2012, 31(5): 136-138.( DING Hu, HU Chao-rong, CHEN Li-qun, JIANG Hai-yan.Steady state response of nonlinear vibration of an axially accelerating viscoelastic Rayleigh beam[J]. Journal of Vibration and Shock , 2012, 31(5): 136-138.(in Chinese))
    [6] David J W, Mithchell L D.Using transfer matrices for parametric system forced response[J]. Transaction of the ASME, Journal of Vibration, Acoustics, Stress and Reliability in Design , 1987, 109(4): 356-360.
    [7] Wu W T, Wickert J A, Griffin J H.Modal analysis of the steady state response of a driven periodic linear system[J]. Journal of Sound and Vibration , 1995, 183(2):297-308.
    [8] Deltombes R, Moraux D, Plessis G, Level P.Forced response of structural dynamic systems with local timedependent stiffness[J]. Journal of Sound and Vibration , 2000, 237(5): 761-773.
    [9] 黄建亮, 陈树辉.外激励力作用下的轴向运动梁非线性振动的联合共振[J].振动工程学报, 2011, 24(5): 455460.(HUANG Jian-liang, CHEN Shu-hui.Combination resonance of nonlinear forced vibration of an axially moving beam[J]. Journal of Vibration Engineering , 2011, 24(5): 455-460.(in Chinese))
    [10] Dimarogonas A D, Papadopoulos C A.Vibration of cracked shafts in bending[J]. Journal of Sound and Vibration , 1983, 91(4): 583-593.
    [11] 王建军, 韩勤锴, 李其汉.参数振动系统频响特性研究[J].振动与冲击, 2010, 29(3): 103-108.(WANG Jian-jun, HAN Qing-kai, LI Qi-han.Frequency response characteristics of parametric vibration system[J].Journal of Vibration and Shock , 2010, 29(3): 103-108.(in Chinese))
    [12] 黄迪山, 程耀东, 童忠钫.参数振动的调制反馈分析[J].浙江大学学报(工学版), 1992(S1) :1624.( HUANG Di-shan, CHENG Yao-dong, TONG Zhong-fan.Modulating feedback analysis for the parametric vibration[J]. Journal of Zhejiang University(Eng Version ), 1992(S1):16-24.
    [13] 黄迪山.复杂参数振动的调制反馈分析[J].应用力学学报, 1995,12(2): 72-77.( HUANG Di-shan.Modulating feedback analysis for complicate parametric vibration[J]. Chinese Journal of Applied Mechanics ,1995,12(2): 72-77.(in Chinese))
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出版历程
  • 收稿日期:  2012-12-24
  • 修回日期:  2013-03-01
  • 刊出日期:  2013-03-15

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