轴向运动变截面黏弹性梁的振动与稳定性分析

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (14) : 107-111.

论文

李成澄赵凤群

作者信息 +

Vibration and stability analysis of axially moving viscoelastic beam with varying section

LI Chengcheng, ZHAO Fengqun

Author information +

文章历史 +

摘要

由D ' Alembert 原理，建立了轴向运动黏弹性变截面梁的运动微分方程，给出了一种重心有理插值DQ法的数值求解方法。对于简支黏弹性变截面梁，用该方法得到了特征方程，获得了变截面梁前两阶无量纲复频率与无量纲轴向运动速度的变化关系。分析了梯形截面梁和抛物形截面梁随轴向运动速度变化的失稳形式，并与等截面梁进行了比较，同时分析了变截面梁的高度比和黏弹性系数对梁动力稳定性的影响。

Abstract

The governing differential equation for axially moving viscoelastic beam with varying section is obtained based on the D ' Alembert principle, and a numerical method of local differential quadrature method based on gravity interpolation is given. For simply supported viscoelastic beam with varying section, the characteristic equation is obtained by using this method and the relation of the first two orders non-dimensional complex frequencies of the beam with non-dimensional axial movement speed are given. The form of instability of the viscoelastic beam with trapezoid cross section and parabolic cross section in different value of axial movement speed is analyzed in detail and compared with uniform beam. The effects of different height ratio and viscoelastic coefficient on the dynamic stability of the beam are discussed.

导出引用

李成澄赵凤群. 轴向运动变截面黏弹性梁的振动与稳定性分析[J]. 振动与冲击, 2016, 35(14): 107-111

LI Chengcheng, ZHAO Fengqun. Vibration and stability analysis of axially moving viscoelastic beam with varying section[J]. Journal of Vibration and Shock, 2016, 35(14): 107-111

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