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空间弹性变形梁动力学的旋量系统理论方法

丁希仑 J·M·塞里格

丁希仑, J·M·塞里格. 空间弹性变形梁动力学的旋量系统理论方法[J]. 应用数学和力学, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011
引用本文: 丁希仑, J·M·塞里格. 空间弹性变形梁动力学的旋量系统理论方法[J]. 应用数学和力学, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011
DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011
Citation: DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011

空间弹性变形梁动力学的旋量系统理论方法

doi: 10.3879/j.issn.1000-0887.2010.09.011
基金项目: 国家自然科学基金资助项目(50275002;50720135503)
详细信息
    作者简介:

    丁希仑(1967- ),男,山东人,教授,博士(联系人.Tel:+86-10-82338005;E-mail:xlding@buaa.edu.cn).

  • 中图分类号: TH112;O302

Screw Theoretic View on Dynamics of Spatially Compliant Beam

  • 摘要: 所谓空间弹性梁,即同时考虑受弯曲、拉伸和扭转等力作用而发生空间变形的梁.借助于刚体运动的旋量理论,引入了“变形旋量”这一概念,进而提出了空间弹性梁的旋量理论.在基本的运动学假设和材料力学理论基础上,分析并给出了梁的空间柔度.接着研究了空间弹性梁的动力学,用旋量理论分析了其动能和势能,从而得到了Lagrange算子.通过对边界条件和变形函数的讨论,进一步运用Rayleigh-Ritz方法计算了系统的振动频率.将空间弹性梁与纯弯曲、扭转或者拉伸等简单变形情况下的特征频率做了对比研究.最后,运用所提出的空间弹性梁理论研究了一关节轴线互相垂直的两空间柔性杆机械臂的动力学,通过动力学仿真发现了关节的刚性运动和空间柔性杆的弹性变形运动之间的耦合影响.该文的研究工作阐明了运用旋量系统理论解决具有空间弹性变形杆件的机构动力学问题的有效性.
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出版历程
  • 收稿日期:  1900-01-01
  • 修回日期:  2010-08-12
  • 刊出日期:  2010-09-15

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