Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 124701-124701.doi: 10.1088/1674-1056/21/12/124701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Parameter design of a liquid-filled sloshing system

钟顺a c, 陈予恕b c   

  1. a School of Civil Engineering, Tianjin University, Tianjin 300072, China;
    b School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;
    c Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, China
  • 收稿日期:2012-04-17 修回日期:2012-05-13 出版日期:2012-11-01 发布日期:2012-11-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10632040) and the Independent Innovation Foundation of Tianjin University.

Parameter design of a liquid-filled sloshing system

Zhong Shun (钟顺)a c, Chen Yu-Shu (陈予恕)b c   

  1. a School of Civil Engineering, Tianjin University, Tianjin 300072, China;
    b School of Mechanical Engineering, Tianjin University, Tianjin 300072, China;
    c Tianjin Key Labortory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, China
  • Received:2012-04-17 Revised:2012-05-13 Online:2012-11-01 Published:2012-11-01
  • Contact: Zhong Shun E-mail:ily_00000@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10632040) and the Independent Innovation Foundation of Tianjin University.

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摘要： The nonlinear governing equations of the liquid sloshing modals in cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviours of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results.

关键词: liquid-filled system, analytical analysis, selection principle, instability

Abstract: The nonlinear governing equations of the liquid sloshing modals in cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviours of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results.

Key words: liquid-filled system, analytical analysis, selection principle, instability

中图分类号:  (Nonlinearity, bifurcation, and symmetry breaking)

  • 47.20.Ky
82.40.Bj (Oscillations, chaos, and bifurcations) 02.30.Hq (Ordinary differential equations)