上海交通大学学报

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2017 , Vol. 51 >Issue 10: 1174 - 1180

DOI: https://doi.org/10.16183/j.cnki.jsjtu.2017.10.004

兵器工业

 基于绝对节点坐标法变截面柔性梁运动稳定性研究

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  •  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

网络出版日期: 2017-10-31

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

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  •  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 published: 2017-10-31

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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

本文引用格式

罗晶晶a,余海东a,赵春璋a,b,王皓a,b .  基于绝对节点坐标法变截面柔性梁运动稳定性研究[J]. 上海交通大学学报, 2017 , 51(10) : 1174 -1180 . DOI: 10.16183/j.cnki.jsjtu.2017.10.004

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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