上海交通大学学报(自然版) ›› 2017, Vol. 51 ›› Issue (10): 1174-1180.doi: 10.16183/j.cnki.jsjtu.2017.10.004

• 兵器工业 • 上一篇    下一篇

 基于绝对节点坐标法变截面柔性梁运动稳定性研究

 罗晶晶a,余海东a,赵春璋a,b,王皓a,b   

  1.  上海交通大学   a. 机械系统与振动国家重点实验室;
    b. 上海市复杂薄板结构数字化制造重点实验室, 上海 200240
  • 出版日期:2017-10-31 发布日期:2017-10-31
  • 基金资助:
     

 Study on Motion Stability of Variable CrossSection Flexible Beams
 Based on the Absolute Nodal Coordinate Formulation

 LUO Jingjinga,YU Haidonga,ZHAO Chunzhanga,b,WANG Haoa,b   

  1.  a. State Key Laboratory of Mechanical System and Vibration; b. Shanghai Key Laboratory of Digital
      Manufacture for Thinwalled Structures, Shanghai Jiao Tong University, Shanghai 200240, China
  • Online:2017-10-31 Published:2017-10-31
  • Supported by:
     

摘要:  基于绝对节点坐标法,考虑变截面梁单元的几何边界特征,利用非线性介质力学方法推导其刚度矩阵,进而建立柔性梁结构动力学方程.基于梁结构运动过程中状态空间方程和Lyapunov理论,提出变截面柔性梁结构运动及稳定性判定方法,研究了材料属性与变截面对梁结构空间运动过程中稳定性的影响.结果表明:当材料弹性模量较小时,变截面梁的稳定性略优于等截面梁;当材料的弹性模量增大,等截面梁单元稳定性大大增加,而变截面梁单元所受影响甚微;当弹性模量的增加达到一定值后,等截面梁的运动也趋于稳定.

关键词:  , 变截面柔性梁, 大变形, 稳定性,  , Lyapunov理论

Abstract:  The boundary features of the variable crosssection beams are taken into consideration and the stiffness matrix is derived based on the nonlinear continuum mechanics. A dynamic model of the beam is established by using the absolute nodal coordinate formulation. The statespace equation of the beam during motion is developed. Based on the Lyapunov theory a criterion of the motion stability of the flexible beams is proposed, and the effects of material properties and variable crosssections are investigated. The results indicate that with a small elastic modulus, the variable crosssection beam shows a better stability than the constant crosssection beam. As the elastic modulus increases, the stability of the constant crosssection becomes better than that of the variable crosssection beam. When the  elastic modulus reaches a certain value, the motion of constant crosssection beam becomes stable.

Key words:  variable crosssection beams, large deformation, kinematic stability, Lyapunov theory

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