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Coupled Systems Mechanics
  Volume 12, Number 1, February 2023 , pages 41-68

Parametric study of the wave dispersion in the hydro-elastic system consisting of an inhomogeneously prestressed hollow cylinder containing compressible inviscid fluid
Surkay D. Akbarov and Gurbaneli J. Veliyev

    The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discreteanalytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.
Key Words
    discrete-analytical method; hydro-elastic hollow cylinder-fluid system; inhomogeneous initial stresses; wave dispersion; compressible fluid
Surkay D. Akbarov: Department of Mechanical Engineering, Yildiz Technical University, 34349, Besiktas, Istanbul, Turkey; Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan,
AZ1141, Baku, Azerbaijan
Gurbaneli J. Veliyev: Baku State University, Baku, Azerbaijan

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