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Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (9): 1167-1178.doi: https://doi.org/10.1007/s10483-012-1613-8

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Free vibration of membrane/bounded incompressible fluid

S. TARIVERDILO1, J. MIRZAPOUR1, M. SHAHMARDANI1, G. REZAZADEH2   

  1. 1. Department of Civil Engineering, Faculty of Engineering, Urmia University, Urmia 15311-57561, Iran;
    2. Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia 15311-57561, Iran
  • 收稿日期:2011-07-26 修回日期:2012-02-13 出版日期:2012-09-10 发布日期:2012-09-10
  • 通讯作者: S. TARIVERDILO, Associate Professor, Ph.D., E-mail: s.tariverdilo@urmia.ac.ir E-mail:s.tariverdilo@urmia.ac.ir

Free vibration of membrane/bounded incompressible fluid

S. TARIVERDILO1, J. MIRZAPOUR1, M. SHAHMARDANI1, G. REZAZADEH2   

  1. 1. Department of Civil Engineering, Faculty of Engineering, Urmia University, Urmia 15311-57561, Iran;
    2. Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia 15311-57561, Iran
  • Received:2011-07-26 Revised:2012-02-13 Online:2012-09-10 Published:2012-09-10

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摘要： Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra-tion of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the sys-tem, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.

关键词: Rayleigh quotient, asymmetric free vibration, membrane, variational formulation, adjoint system, impulse transfer, regular transform

Abstract: Vibration of a circular membrane in contact with a fluid has extensive applications in industry. The natural vibration frequencies for the asymmetric free vibra-tion of a circular membrane in contact with a bounded incompressible fluid are derived in this paper. Considering small oscillations induced by the membrane vibration in an incompressible and inviscid fluid, the velocity potential function is used to describe the fluid field. Two approaches are used to derive the free vibration frequencies of the sys-tem, which include a variational formulation and an approximate solution employing the Rayleigh quotient method. A good correlation is found between free vibration frequencies evaluated by these methods. Finally, the effects of the fluid depth, the mass density, and the radial tension on the free vibration frequencies of the coupled system are investigated.

Key words: Rayleigh quotient, asymmetric free vibration, membrane, variational formulation, adjoint system, impulse transfer, regular transform

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