弹性压应力波下轴向功能梯度变截面梁动力压曲稳定分析

陈得良, 汪亚运, 彭旭龙, 周露

振动与冲击 ›› 2017, Vol. 36 ›› Issue (13) : 27-32.

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PDF(989 KB)
振动与冲击 ›› 2017, Vol. 36 ›› Issue (13) : 27-32.
论文

弹性压应力波下轴向功能梯度变截面梁动力压曲稳定分析

  • 陈得良, 汪亚运, 彭旭龙, 周露
作者信息 +

Dynamic buckling of axially functionally graded beam with non-uniform cross-section under elastic compression wave

  • CHEN De-liang  WANG Ya-yun  PENG Xu-long  ZHOU Lu
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摘要

基于微元法以及能量守恒原理,导出了轴向功能梯度变截面梁屈曲微分控制方程及应力波波前附加边界条件,研究了轴向功能梯度变截面梁屈曲与压应力波耦合动力屈曲问题。采用较为简单的数值方法,即将位移函数按Taylor级数或是Chebyshev多项式展开,从而将轴向功能梯度变截面梁屈曲问题的变系数微分控制方程转化为含参量的线性代数方程组,进而得到了含时间参量的动力屈曲问题特征方程,随后对轴向功能梯度变截面梁动力屈曲问题进行了数值研究,探讨了变截面和材料不均匀性对系统屈曲临界力参数的影响。研究表明,该数值方法具有很好的精度和收敛性。

Abstract

In the paper, the dynamic buckling of axially functionally graded beams under coupled stress wave propagating and dynamic buckling is investigated. The bucking governing equation and the boundary conditions at the compression stress wave front for a axially functionally graded beams are established based on the Infinitesimal section force balance condition and the principle of conservation of energy. A numerical method is introduced to transfer the varying coefficients differential equation into the linear algebraic equation sets, in which the displacement function expressed with Taylor/Chebyshev polynomials expansion. And then the eigen-equation for the axially functionally graded beams with non-uniform cross-section is obtained. Moreover, a numerical investigation for dynamic buckling of the axially functionally graded beams is carried out discussing the effects of variable cross-section and material inhomogeneity on critical buckling force parameters. The results shows that the present method has good accuracy and convergence.
 

关键词

功能梯度梁 / 变截面 / 压应力波 / Taylor级数/Chebyshev多项式 / 动力屈曲

Key words

axially functionally graded beams / non-uniform cross-section / compression wave / Taylor/Chebyshev polynomials / dynamic buckling 

引用本文

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陈得良, 汪亚运, 彭旭龙, 周露. 弹性压应力波下轴向功能梯度变截面梁动力压曲稳定分析[J]. 振动与冲击, 2017, 36(13): 27-32
CHEN De-liang WANG Ya-yun PENG Xu-long ZHOU Lu. Dynamic buckling of axially functionally graded beam with non-uniform cross-section under elastic compression wave[J]. Journal of Vibration and Shock, 2017, 36(13): 27-32

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