S.Tariverdilo, J.Mirzapour, M.Shahmardani, Gh.Rezazadeh. Free Vibration of Membrane/Bounded Incompressible Fluid[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1091-1101. doi: 10.3879/j.issn.1000-0887.2012.09.006
Citation: S.Tariverdilo, J.Mirzapour, M.Shahmardani, Gh.Rezazadeh. Free Vibration of Membrane/Bounded Incompressible Fluid[J]. Applied Mathematics and Mechanics, 2012, 33(9): 1091-1101. doi: 10.3879/j.issn.1000-0887.2012.09.006

Free Vibration of Membrane/Bounded Incompressible Fluid

doi: 10.3879/j.issn.1000-0887.2012.09.006
  • Received Date: 2011-07-26
  • Rev Recd Date: 2012-02-13
  • Publish Date: 2012-09-15
  • Vibration of circular membrane in contact with fluid had extensive applications in the industry. The natural vibration frequencies for asymmetric free vibration of circular membrane in contact with incompressible bounded fluid were derived. Considering small oscillations induced by the membrane vibration in incompressible and inviscid fluid, velocity potential function was used to describe the fluid field. Two approaches were used to derive the free vibration frequencies of the system. These included a variational formulation and an approximate solution employing the Rayleigh quotient method. Good correlation was found between free vibration frequencies evaluated using the two methods. Finally, the effects of the fluid depth and mass density, and radial tension on the free vibration frequencies of the coupled system were investigated.
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