Investigation of power-type variational principles in liquid-filled system

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• 作者：Haiyan Song ; Lifu Liang
• 关键词：hydrodynamics ; rigid ; body dynamics ; elasto ; dynamics ; coupling dynamics ; power ; type variational principle ; O313.3 ; O357.1 ; 70E55 ; 74F10
• 刊名：Applied Mathematics and Mechanics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：36
• 期：12
• 页码：1651-1662
• 全文大小：156 KB
• 参考文献：[1]Cheng, C. J. Chien Wei-zang鈥檚 contributions to mechanics and applied mathematics (in Chinese). Advances in Mechanics, 40, 480鈥?94 (2010)
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  [15]Paul, G. H. Conceptual Physics, Addison-Wesley, New Jersey (2010)
  
• 作者单位：Haiyan Song (1)
  Lifu Liang (1)
  
  1. School of Aerospace and Civil Engineering, Harbin Engineering University, Harbin, 150001, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Applications of Mathematics
  Mechanics
  Mathematical Modeling and IndustrialMathematics
  Chinese Library of Science
  
• 出版者：Shanghai University, in co-publication with Springer
• ISSN：1573-2754

文摘

Starting from the basic equations of hydrodynamics, the maximum powertype variational principle of the hydrodynamics of viscous fluids was established by Weizang CHIEN in 1984. Through long-term research, it is clarified that the maximum power-type variational principle coincides with the Jourdian principle, which is one of the common principles for analytical mechanics. In the paper, the power-type variational principle is extended to rigid-body dynamics, elasto-dynamics, and rigid-elastic-liquid coupling dynamics. The governing equations of the rigid-elastic-liquid coupling dynamics in the liquid-filled system are obtained by deriving the stationary value conditions. The results show that, with the power-type variational principles studied directly in the state space, some transformations in the time domain space may be omitted in the establishing process, and the rigid-elastic-liquid coupling dynamics can be easily numerically modeled. Moreover, the analysis of the coupling dynamics in the liquid-filled system in this paper agrees well with the numerical analyses of the coupling dynamics in the liquid-filled system offered in the literatures. Keywords hydrodynamics rigid-body dynamics elasto-dynamics coupling dynamics power-type variational principle