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Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (5): 607-620.doi: https://doi.org/10.1007/s10483-014-1816-7

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Transverse vibrations of arbitrary non-uniform beams

郭树起1 杨绍普2   

  1. 1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China;
    2. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China
  • 收稿日期:2013-03-25 修回日期:2013-06-18 出版日期:2014-05-01 发布日期:2014-05-01

Transverse vibrations of arbitrary non-uniform beams

GUO Shu-Qi1, YANG Shao-Pu2   

  1. 1. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China;
    2. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043, P. R. China
  • Received:2013-03-25 Revised:2013-06-18 Online:2014-05-01 Published:2014-05-01

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被引次数

1

摘要： Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

关键词: transverse vibration, non-uniform beam, series solution, convergence

Abstract: Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.

Key words: transverse vibration, non-uniform beam, convergence, series solution

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