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用微分求积法分析轴向加速粘弹性梁的非线性动力学行为 被引量：1

ANALYSIS ON NONLINEAR DYNAMICS OF AN AXIALLY ACCELERATING VISCOELASTIC BEAM USING DQM
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摘要 用微分求积数值方法求解了轴向加速粘弹性梁的横向振动控制方程,其方程是一复杂的非线性偏微分方程.并在数值结果的基础上利用分叉图分析了轴向定常加速度以及轴向加速度变化幅值对轴向加速粘弹性梁的非线性动力学行为的影响. The differential quadrature method （DQM） was developed to solve numerically the nonlinear partial differential equation of the nonlinear transverse vibration of an axially accelerating viscoelastic beam. Based on the numerical solutions, the nonlinear dynamical behaviors, such as bifurcations and chaotic motions of the nonlinear system, were investigated by use of Poincare map, phase portrait.
作者 王冬梅 张伟 刘燕
机构地区 北京工业大学机电学院 山东济宁学院数学系 西华师范大学物电学院
出处 《动力学与控制学报》 2013年第1期42-45,共4页 Journal of Dynamics and Control
基金 国家自然科学基金重大项目资助(11290152)和国家自然科学基金(10732020 11072008)资助项目~~
关键词 非线性偏微分方程 数值解 混沌 分叉 微分求积法 DQM, nonlinear partial-differential equation, numerical solution, chaos, bifurcations
分类号 O343 [理学—固体力学] O241.4 [理学—计算数学]
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参考文献7

  • 1Ravindra B, Zhu W D. Low dimensional chaotic response of axially accelerating continuum in the supercritical re- gime. Archive of Applied Mechanics, 1998,68 : 195 - 205.
  • 2Marynowski K, Kapitaniak T. Kelvin-Voigt versus Burgers internal damping in modeling of axially moving viscoelastic web. International Journal of Non-linear Mechanics, 2002, 37:1147-1161.
  • 3Yang X D, Chen L Q. Bifurcation and chaos of an axially accelerating viscoelastic beam. Chaos, Solitons and Frac- tals, 2005, 23(1) :249 -258.
  • 4Chen L H, Zhang W, Yang F H. Nonlinear dynamics of higher-dimensional system for an axially accelerating visco- elastic beam with in-plane and out-of-plane vibrations. Journal of Sound and Vibration, 2010,329:5321 - 5345.
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同被引文献15

  • 1吴俊,陈立群.轴向变速运动弦线的非线性振动的稳态响应及其稳定性[J].应用数学和力学,2004,25(9):917-926. 被引量：12
  • 2周银锋,王忠民.轴向运动粘弹性板的横向振动特性[J].应用数学和力学,2007,28(2):191-199. 被引量：28
  • 3Shin C, Chung J, Kim W. Dynamic characteristics of the out- of-plane vibration for an axially moving membrane [ J ]. Journal of Sound and Vibration, 2005,286 : 1019 - 1031.
  • 4Kulachenko A, Gradin P, Koivurova H. Modeling the dynamical behaviour of a paper webpart I [ J ]. Computers and Structures, 2007, 85( 1 ) : 131 -147.
  • 5Kulachenko A, Gradin P, Koivurova H. Modeling the dynamical behaviour of a paper webpart II[ J ]. Computers and Structures, 2007, 85(2) : 148 -157.
  • 6Wu Ji-mei, Wu Qiu-min, Ma Li-e,et al. Parameter vibration and dynamic stabihty of the printing paper web with variable speed [ J ]. Journal of Low Frequency Noise, Vibration and Active Control, 2010, 29 (4) : 281 -291.
  • 7Nguyen Q C, Hong K S. Stabilization of an axially moving web via regulation of axial velocity[J]. Journal of Sound and Vibration, 2011, 330(20) : 4676 -4688.
  • 8Nguyen Q C, Hong K S. Transverse vibration control ofaxially moving membranes by regulation of axial velocity [ J ]. IEEE Transactions on Control Systems Technology, 2012, 20(4) : 1124 -1131.
  • 9Ma Li-e, Wu Ji-mei, Mei Xue-song, et al. Active vibration control of moving wed with varying density [ J ]. Journal of Low Frequency Noise, Vibration and Active Control, 2013, 32(4) : 323 -334.
  • 10Wu Ji-mei, Lei Wen-jiao, Wu Qiu-min, et al. Transverse vibration characteristics and stability of a moving membrane with elastic supports [J].Journal of Low Frequency Noise, Vibration and Active Control, 2014, 33(1) : 65 -78.

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动力学与控制学报
2013年 第1期

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