Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity

  • Authors

    • Hilal Essaouini Faculty of Sciences; University Abdelmalek Essaadi; Tetuan.
    • Pierre Capodanno
    2019-08-25
    https://doi.org/10.14419/gjma.v7i1.26540
  • Gas Dynamics, Free Boundaries, Capillarity (Surface Tension), Small Oscillations, Variational Method.

  • Abstract

    This paper deals with the mathematical study of the small motions of a system formed by a cylindrical liquid column bounded by two parallel circular rings and an internal cylindrical column constituted by a barotropic gas under zero gravity. From the equations of motion, the authors deduce a variational equation. Then, the study of the small oscillations depends on the coerciveness of a hermitian form that appears in this equation. It is proved that this last problem is reduced to an auxiliary eigenvalues problem. The discussion shows that, under a simple geometric condition, the problem is a classical vibration problem.

     

     

  • References

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  • How to Cite

    Essaouini, H., & Capodanno, P. (2019). Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity. Global Journal of Mathematical Analysis, 7(1), 4-14. https://doi.org/10.14419/gjma.v7i1.26540

    Received date: 2019-01-26

    Accepted date: 2019-07-06

    Published date: 2019-08-25