北京航空航天大学学报 ›› 2014, Vol. 40 ›› Issue (6): 829-833.doi: 10.13700/j.bh.1001-5965.2013.0400

• 论文 • 上一篇    下一篇

变质量梁的自适应Newmark法

王宇楠, 邢誉峰   

  1. 北京航空航天大学 固体力学研究所, 北京 100191
  • 收稿日期:2013-07-04 出版日期:2014-06-20 发布日期:2014-07-03
  • 作者简介:王宇楠(1988- ),女,辽宁沈阳人,硕士生,wayunan@gmail.com.
  • 基金资助:

    国家自然科学基金资助项目(1172028,11372021)

Self-adaptive Newmark method of variable-mass beam dynamic system

Wang Yunan, Xing Yufeng   

  1. Institute of Solid Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2013-07-04 Online:2014-06-20 Published:2014-07-03

摘要: 用变质量梁来模拟推进剂减少的液体火箭.先以一弹簧-变质量小球系统为例,用其求解结果与解析解进行比较.再以时不变的简支梁为算例,确定多自由度系统下与结构动特性协同的自适应Newmark方法中的参数选取.最后用时变的简支梁模型模拟贮箱质量的实际变化方式,运用与结构动特性协同的自适应Newmark方法、模态叠加法、Newmark平均加速度方法(NMA法)和Fox-Goodwin方法(NMF法)对其求解.比较结果证明自适应Newmark算法对于时变系统的适用性,尤其具有高精度特性.

Abstract: Variable-mass beam was used to model launch vehicle. Firstly the results of a spring-variable-mass ball system were compared with the analytical solutions. Then by using an example of a constant-mass beam, the parameters of the self-adaptive Newmark method were determined. At last the practical procedure of propellant decreasing and its effects on the transverse vibration were taken into account in a variable-mass beam. The self-adaptive Newmark method whose parameters depend on the inherent frequency of dynamic system, phase error and spectral radius of the method was employed to solve the dynamic responses of a variable-mass beam system, and the obtained results were compared with those of the analytical solutions by mode superposition method, average acceleration method (NMA) and Fox-Goodwin method (NMF). The comparison shows that the self-adaptive Newmark method is applicable to the variable-mass system, and it is more accurate than the methods used for comparison, especially the phase accuracy.

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