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大变形轴向运动梁的精确动力学模型

刘延柱

刘延柱. 大变形轴向运动梁的精确动力学模型[J]. 力学学报, 2012, 44(5): 832-838. doi: 10.6052/0459-1879-12-117
引用本文: 刘延柱. 大变形轴向运动梁的精确动力学模型[J]. 力学学报, 2012, 44(5): 832-838. doi: 10.6052/0459-1879-12-117
Liu Yanzhu. EXACT DYNAMICAL MODEL OF AXIALLY MOVING BEAM WITH LARGE DEFORMATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(5): 832-838. doi: 10.6052/0459-1879-12-117
Citation: Liu Yanzhu. EXACT DYNAMICAL MODEL OF AXIALLY MOVING BEAM WITH LARGE DEFORMATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(5): 832-838. doi: 10.6052/0459-1879-12-117

大变形轴向运动梁的精确动力学模型

doi: 10.6052/0459-1879-12-117
基金项目: 国家自然科学基金资助项目(10972143).
详细信息
    通讯作者:

    刘延柱

  • 中图分类号: O317,O343

EXACT DYNAMICAL MODEL OF AXIALLY MOVING BEAM WITH LARGE DEFORMATION

Funds: The project was supported by the National Natural Science Foundation of China (10972143).
  • 摘要: 轴向运动梁的横向振动是具有实际工程背景的动力学问题.该文应用Cosserat弹性杆模型讨论圆截面轴向运动梁的动力学建模及其运动稳定性.以沿梁中心线的弧坐标代替方向固定的坐标轴,根据梁截面的姿态随弧坐标和时间的变化确定梁的变形过程.从欧拉的速度场概念出发,考虑梁截面转动的惯性效应和剪切变形,建立大变形轴向运动梁的动力学方程.其小变形特例为轴向运动的三维Timoshenko梁.基于该模型分析了轴向运动梁准稳态运动的静态和动态稳定性,导出可导致失稳的临界轴向速度.证明空间域内的欧拉稳定性条件是时间域内的Lyapunov稳定性的必要条件.

     

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出版历程
  • 收稿日期:  2012-05-02
  • 修回日期:  2012-07-11
  • 刊出日期:  2012-09-18

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