MA Guo-liang, XU Ming-long, CHEN Li-qun, DING Hu. Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass[J]. Applied Mathematics and Mechanics, 2015, 36(9): 897-904. doi: 10.3879/j.issn.1000-0887.2015.09.001
Citation: MA Guo-liang, XU Ming-long, CHEN Li-qun, DING Hu. Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass[J]. Applied Mathematics and Mechanics, 2015, 36(9): 897-904. doi: 10.3879/j.issn.1000-0887.2015.09.001

Vibration Characteristics of an Axially Moving Variable Length Beam With a Tip Mass

doi: 10.3879/j.issn.1000-0887.2015.09.001
Funds:  The National Natural Science Foundation of China(11172229)
  • Received Date: 2015-04-24
  • Rev Recd Date: 2015-06-15
  • Publish Date: 2015-09-15
  • A semi-analytical method and a numerical method were used to investigate the vibration characteristics of an axially moving variable length (velocity) beam with a tip mass. First, the equation of transverse free vibration for the axially moving Euler beam was simplified. The eigenequation was derived with the complex modal analysis method. Moreover, the frequency equation was obtained under the boundary conditions with a tip mass. The numerical method was used to calculate the natural frequencies and modal shapes. Then, the equation of transverse free vibration was also derived with the finite element method (FEM). The complex eigenvalues and eigenvectors were obtained as solutions to the complex matrix equation, and the complex modal displacements were given through combination with the shape functions. Finally, the results from these 2 methods were comparatively analyzed. The numerical example illustrates that different velocities and tip masses influence the beam vibration characteristics significantly. The calculated results from the 2 methods are close to each other and effective.
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  • [1]
    Mote Jr C D. Dynamic stability of axially moving materals[J]. Shock and Vibration,1972,4(4): 2-11.
    [2]
    Tabarrok B, Leech C M, Kim Y I. On the dynamics of an axially moving beam[J]. Journal of the Franklin Institute,1974,297(3): 201-220.
    [3]
    Oz H R, Pakdemirli M. Vibrations of an axially moving beam with time dependent velocity[J]. Journal of Sound and Vibration,1999,227(2): 239-257.
    [4]
    Suweken G, Van Horssen W T. On the transversal vibrations of a conveyor belt with a low and time-varying velocity—part II: the beam-like case[J]. Journal of Sound and Vibration,2003,267(5): 1007-1027.
    [5]
    Sandilo S H, Van Horssen W T. On boundary damping for an axially moving beam and on the variable length induced vibrations of an elevator cable[C]//In Proceedings of the 7th European Nonlinear Oscillations Conference.Rome, Italy, 2011.
    [6]
    Ghayesh M H, Amabili M. Steady-state transverse response of an axially moving beam with time-dependent axial speed[J]. International Journal of Non-Linear Mechanics,2013,49: 40-49.
    [7]
    Marynowski K, Kapitaniak T. Dynamics of axially moving continua[J]. International Journal of Mechanical Sciences,2014,81: 26-41.
    [8]
    Fung R F, Lu P Y, Tseng C C. Non-linearly dynamicmodeling of an axially moving beam with a tip mass[J]. Journal of Sound and Vibration,1998,218(4): 559-571.
    [9]
    王亮, 陈怀海, 贺旭东, 游伟倩. 轴向运动变长度悬臂梁的振动控制[J]. 振动工程学报, 2009,22(6): 565-570.(WANG Liang, CHEN Huai-hai, HE Xu-dong, YOU Wei-qian. Vibration control of an axially moving cantilever beam with varying length[J]. Journal of Vibration Engineering,2009,22(6): 565-570.(in Chinese))
    [10]
    刘宁, 杨国来. 移动质量作用下轴向运动悬臂梁振动特性分析[J]. 振动与冲击, 2012,31(3): 102-105.(LIU Ning, YANG Guo-lai. Vibration property analysis of axially moving cantilever beam considering the effect of moving mass[J]. Journal of Vibration and Shock,2012,31(3): 102-105.(in Chinese))
    [11]
    CHEN Li-qun, DING Hu, Lim C W. Principal parametric resonance of axially accelerating viscoelastic beams: multi-scale analysis and differential quadrature verification[J]. Shock and Vibration,2012,19(4): 527-543.
    [12]
    王波. 轴向运动三参数黏弹性梁弱受迫振动的渐近分析[J]. 应用数学和力学, 2012,33(6): 771-780.(WANG Bo. Asymptotic analysis on weakly forced vibration of an axially moving viscoelastic beam constituted by standard linear solid model [J]. Applied Mathematics and Mechanics,2012,33(6): 771-780.(in Chinese))
    [13]
    Stylianou M, Tabarrok B. Finite element analysis of an axially moving beam—part I: time integration[J]. Journal of Sound and Vibration,1994,178(4): 433-453.
    [14]
    Cepon G, BolteZar M. Computing the dynamic response of an axially moving continuum[J]. Journal of Sound and Vibration,2007,300(1/2): 316-329.
    [15]
    Piovan M T, Sampaio R. Vibrations of axially moving flexible beams made of functionally graded materials[J]. Thin-Walled Structures,2008,46(2): 112-121.
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