Liquid Induced Vibrations of Truncated Elastic Conical Shells with Elastic and Rigid Bottoms

  • Authors

    • Yury V. Naumenko
    • Vasyl I. Gnitko
    • Elena A. Strelnikova
    2018-04-20
    https://doi.org/10.14419/ijet.v7i2.23.15327
  • Boundary element method, liquid sloshing, truncated conical shells, rigid and elastic bottoms.

  • A method of estimating natural modes and frequencies of vibrations for elastic shells of revolution conveying a liquid is proposed. The vibration modes of the liquid-filled elastic shells are presented as linear combinations of their own vibration modes without liquid. The explicit expression for fluid pressure is defined using Bernoulli’s integral and potential theory suppositions. Non-penetration, kinematic, and dynamic boundary conditions are applied at the shell walls and on a free liquid surface, respectively. The solution of the hydro-elasticity problem is found out using an effective technique based on coupled finite and boundary element methods. Computational vibration analysis of elastic truncated conical shells with different fixation conditions is accomplished. Sloshing and elastic walls frequencies and modes of liquid-filled truncated conical tanks are estimated. Both rigid and elastic bottoms of shells are considered. Some examples of numerical estimations are provided to testify the efficiency of the developed method

     

     

  • References

    1. [1] Zhang Y.L., Gorman D.G. & Reese,J.M. (2003), Vibration of prestressed thin cylindrical shells conveying fluid. Thin-Walled Structures, 41, 1103–1127.

      [2] Kashani B.K., Sani A.A. (2016), Free vibration analysis of horizontal cylindrical shells including sloshing effect utilizing polar finite elements, European Journal of Mechanics - A/Solids, 58 187-201.

      [3] Gnitko V., Degtyariov K., Naumenko V., Strelnikova E. (2017), BEM and FEM analysis of the fluid-structure Interaction in tanks with baffles. Int. Journal of Computational Methods and Experimental Measurements, 5(3), 317-328..

      [4] Liew K.M., Ng T.Y., Zhao X. (2005), Free vibration analysis of conical shells via the element-free kp-Ritz method J. Sound Vib., 281, 627-645.

      [5] Ramesh T.C., Ganesan N. (1993), A finite element based on a discrete layer theory for the free vibration analysis of conical shells. J. Sound Vib., 166 (3), 531-538.

      [6] Shu C. (1996), An efficient approach for free vibration analysis of conical shells. Int. J. Mech. Sci., 38 (8-9), 935-949.

      [7] Kerboua Y., Lakis A.A., Hmila M. (2010),Vibration analysis of truncated conical shells subjected to flowing fluid. Applied Mathematical Modelling, 34 (3), 791-809.

      [8] Ravnik J., Strelnikova E., Gnitko V., Degtyarev K., Ogorodnyk U. (2016), BEM and FEM analysis of fluid-structure interaction in a double tank, Engineering Analysis with Boundary Elements, 67, 13-25.

      [9] Levitin M., Vassiliev D. (1996), Vibrations of Shells Contacting Fluid: Asymptotic Analysis. Acoustic Interactions with Submerged Elastic Structures, 5, 310-332.

      [10] Degtyarev K., Glushich P., Gnitko V., Strelnikova E. (2015), Numerical Simulation of Free Liquid-Induced Vibrations in Elastic Shells. Int. Journal of Modern Physics and Applications. 1(4), 159-168.

      [11] Brebbia, C.A., Telles, J.C.F. & Wrobel, L.C. Boundary Element Techniques, Springer-Verlag: Berlin and New York, (1984), pp.70-74.

      [12] Degtyarev K., Gnitko V., NaumenkoV., Strelnikova E. (2016), Reduced Boundary Element Method for Liquid Sloshing Analysis of Cylindrical and Conical Tanks with Baffles. Int. Journal of Electronic Engineering and Computer Sciences 1(1), 14-27.

  • Downloads

  • How to Cite

    V. Naumenko, Y., I. Gnitko, V., & A. Strelnikova, E. (2018). Liquid Induced Vibrations of Truncated Elastic Conical Shells with Elastic and Rigid Bottoms. International Journal of Engineering & Technology, 7(2.23), 335-339. https://doi.org/10.14419/ijet.v7i2.23.15327