Advertisement

Meccanica

, Volume 51, Issue 9, pp 2045–2058 | Cite as

Coupled response of liquid in a rigid cylindrical container equipped with an elastic annular baffle

  • Jiadong Wang
  • Ding Zhou
  • Weiqing Liu
Article
  • 180 Downloads

Abstract

The coupled dynamic response of liquid partially filled in a rigid cylindrical container equipped with an elastic baffle under lateral excitation has been studied. Firstly, the liquid domain is divided into four simple sub-domains so that the non-convex liquid domain changes to four convex sub-domains. Therefore, the liquid velocity potential in each liquid sub-domain has continuous boundary conditions of class C1. Based on the superposition principle, the analytical solution of the liquid velocity potential corresponding to each liquid sub-domain is obtained by means of the method of separation of variables. Then, the wet mode of the elastic annular baffle is expressed in terms of the dry-modal functions. The free surface wave equation, the interface equations and the coupled liquid-baffle vibration equations are all expressed in terms of the Fourier series along the liquid height and the Bessel series in the radial direction, respectively. The orthogonality among the coupled modes of the system is demonstrated. Finally, the total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The coupled dynamic response equation of the liquid-baffle system is established by combining the free surface wave equation and the governing vibration equation of the baffle. The surface wave height, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment for a container subjected to lateral excitations are discussed in detail.

Keywords

Elastic baffle Cylindrical container Coupled mode Semi-analytical method Dynamic response 

Notes

Acknowledgments

The financial supports from National Natural Science Foundation of China, Grant No. 11172123 and Key Science Research Project of Universities of Jiangsu Province, Grant No. 12KJA580002 are greatly appreciated.

References

  1. 1.
    Faltinsen OM, Timokha AN (2009) Sloshing. Cambridge University Press, CambridgeMATHGoogle Scholar
  2. 2.
    Goudarzia MA, Sabbagh-Yazdi SR (2012) Investigation of nonlinear sloshing effects in seismically excited tanks. Soil Dyn Earthq Eng 12:355–365CrossRefGoogle Scholar
  3. 3.
    Bauer HF (1981) Hydroelastic vibrations in a rectangular container. Int J Solids Struct 17:639–652ADSCrossRefMATHGoogle Scholar
  4. 4.
    Bauer HF (1995) Coupled frequencies of a liquid in a circular cylindrical container with elastic liquid surface cover. J Sound Vib 180:689–704ADSCrossRefGoogle Scholar
  5. 5.
    Cheung YK, Zhou D (2000) Coupled vibratory characteristics of a rectangular container bottom plate. J Fluids Struct 14:339–357CrossRefGoogle Scholar
  6. 6.
    Zhou D, Cheung YK (2000) Vibration of vertical rectangular plate in contact with water on one side. Earthq Eng Struct Dyn 29:693–710CrossRefGoogle Scholar
  7. 7.
    Cheung YK, Zhou D (2002) Hydroelastic vibration of a circular container bottom plate using the Galerkin method. J Fluids Struct 16:561–580CrossRefGoogle Scholar
  8. 8.
    Kim YW, Lee YS (2005) Coupled vibration analysis of liquid-filled rigid cylindrical storage tank with an annular plate cover. J Sound Vib 279:217–235ADSCrossRefGoogle Scholar
  9. 9.
    Kwak MK, Kim KC (1991) Axisymmetric vibration of circular plates in contact with fluid. J Sound Vib 146:381–389ADSCrossRefGoogle Scholar
  10. 10.
    Meylan MH (1997) The forced vibration of a thin plate floating on an infinite liquid. J Sound Vib 205:581–591ADSCrossRefMATHGoogle Scholar
  11. 11.
    Amabili M, Kwak MK (1999) Vibration of circular plates on fluid surface effect of surface waves. J Sound Vib 226:407–424ADSCrossRefGoogle Scholar
  12. 12.
    Evans DV, Mclver P (1987) Resonant frequencies in a container with a vertical baffle. J Fluid Mech 175:295–307ADSCrossRefMATHGoogle Scholar
  13. 13.
    Watson EBB, Evans DV (1991) Resonant frequencies of a fluid in containers with internal bodies. J Eng Math 25:115–135MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Choun Y, Yun C (1996) Sloshing characteristics in rectangular tanks with a submerged block. Comput Struct 61:401–413CrossRefGoogle Scholar
  15. 15.
    Gedikli A, Ergüven ME (1999) Seismic analysis of a liquid storage tank with a baffle. J Sound Vib 223:141–155ADSCrossRefGoogle Scholar
  16. 16.
    Cho JR, Lee HW, Kim KW (2002) Free vibration analysis of baffled liquid-storage tanks by the structural-acoustic finite element formulation. J Sound Vib 258:847–866ADSCrossRefGoogle Scholar
  17. 17.
    Biswal KC, Bhattacharyya SK, Sinha PK (2003) Free vibration analysis of liquid filled tank with baffles. J Sound Vib 259:177–192ADSCrossRefGoogle Scholar
  18. 18.
    Biswal KC, Bhattacharyya SK, Sinha PK (2004) Dynamic response analysis of a liquid-filled cylindrical tank with annular baffle. J Sound Vib 274:13–37ADSCrossRefGoogle Scholar
  19. 19.
    Maleki A, Ziyaeifar M (2008) Sloshing damping in cylindrical liquid storage tanks with baffles. J Sound Vib 311:372–385ADSCrossRefGoogle Scholar
  20. 20.
    Panigrahy PK, Saha UK, Maity D (2009) Experimental studies on sloshing behavior due to horizontal movement of liquids in baffled tanks. Ocean Eng 36:213–222CrossRefGoogle Scholar
  21. 21.
    Askari E, Daneshmand F (2009) Coupled vibration of a partially fluid-filled cylindrical container with a cylindrical internal body. J Fluids Struct 25:389–405CrossRefGoogle Scholar
  22. 22.
    Askari E, Jeong KH, Amabili M (2013) Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface. J Sound Vib 332:3064–3085ADSCrossRefGoogle Scholar
  23. 23.
    Wang JD, Zhou D, Liu WQ (2012) Sloshing of liquid in rigid cylindrical container with a rigid annular baffle. Part I: free vibration. Shock Vib 19:1185–1203CrossRefGoogle Scholar
  24. 24.
    Wang JD, Lo SH, Zhou D (2012) Liquid sloshing in rigid cylindrical container with multiple rigid annular baffles: free vibration. J Fluids Struct 34:138–156CrossRefGoogle Scholar
  25. 25.
    Wang JD, Zhou D, Liu WQ (2012) Sloshing of liquid in rigid cylindrical container with a rigid annular baffle. Part II: lateral vibration. Shock Vib 19:1205–1222CrossRefGoogle Scholar
  26. 26.
    Wang JD, Lo SH, Zhou D (2013) Liquid sloshing in rigid cylindrical container with multiple rigid annular baffles: lateral excitations. J Fluids Struct 42:421–436CrossRefGoogle Scholar
  27. 27.
    Wang JD, Zhou D, Liu WQ (2012) Study on coupled vibration characteristics of a cylindrical tank with a flexible annular baffle. Eng Mech 29(6):270–278 (in Chinese) Google Scholar
  28. 28.
    Wang JD, Zhou D, Liu WQ (2012) Study on coupled vibration characteristics of a cylindrical container with multiple elastic annular baffles. Sci China Technol Sci 55(12):3292–3301CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.College of Civil EngineeringNanjing Tech UniversityNanjingChina

Personalised recommendations