Journal of Mechanical Science and Technology

, Volume 33, Issue 6, pp 2527–2536 | Cite as

An efficient method to improve the stability of submerged functionally graded cylindrical shell

  • Rong LiEmail author
  • Linxia Liu
  • Bin Liang
  • Meng Yang


An efficient method is presented to improve the stability of a submerged functionally graded (FG) cylindrical shell which is subjected to external hydrostatic pressure. To improve stability while satisfying the application requirements for shell thickness, we focused on the optimum value of the power-law exponent to maximize the critical hydrostatic pressure. The optimum value of the power-law exponent is obtained from an analysis of the influence factors on critical pressure. The results show that the critical pressure can be greatly increased by using the optimum value of the power-law exponent, and the growth rate of critical pressure is almost constant independent of the shell geometry and boundary condition. The advantage of the present method in reducing the shell thickness is illustrated by examples. In addition, the present method is applicable to all kinds of material combinations.


Power-law exponent Critical pressure Functionally graded materials Cylindrical shell Shell thickness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the National Natural Science Foundation of China (Contract Nos: 51105132 and 11402077) and the Doctoral Scientific Research Foundation of Henan University of Science and Technology (Contract No: 4007-13480032).


  1. [1]
    S. Toros and K. Altinel, Contribution of functionally graded material modelling on finite element simulation of rod end parts in automotive steering system, J. of Mechanical Science and Technology, 30 (7) (2016) 3137–3141.CrossRefGoogle Scholar
  2. [2]
    M. Arefi, Nonlinear thermal analysis of a hollow functionally graded cylinder with temperature-variable material properties, J. of Applied Mechanics and Technical Physics, 56 (2) (2015) 267–273.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Y. T. Beni, F. Mehralian and H. Razavi, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory, Composite Structures, 120 (2015) 65–78.CrossRefGoogle Scholar
  4. [4]
    P. T. Thang, N. D. Duc and T. Nguyen-Thoi, Thermome-chanical buckling and post-buckling of cylindrical shell with functionally graded coatings and reinforced by stringers, Aerospace Science and Technology, 66 (2017) 392–401.CrossRefGoogle Scholar
  5. [5]
    M. Fadaee and M. R. Ilkhani, Closed-form solution for freely vibrating functionally graded thick doubly curved panel-a new generic approach, Latin American J. of Solids and Structures, 12 (9) (2015) 1748–1770.CrossRefGoogle Scholar
  6. [6]
    J. Zhang, W. Li, J. Yu, Q. Zhang, S. Cui, Y. Li, S. Li and G. Chen, Development of a Virtual Platform for telepresence control of an underwater manipulator mounted on a submersible vehicle, IEEE Transactions on Industrial Electronics, 64 (2) (2017) 1716–1727.CrossRefGoogle Scholar
  7. [7]
    S. Gupta, H. Matos, J. M. LeBlanc and A. Shukla, Shock initiated instabilities in underwater cylindrical structures, J. of the Mechanics and Physics of Solids, 95 (2016) 188–212.CrossRefGoogle Scholar
  8. [8]
    X. Weng, S. Zhu, H. Dai, Y. Fu and Y. Mao, Mechanical and acoustic response of an underwater structure subjected to mechanical excitation, Acta Mechanica Solida Sinica, 27 (3) (2014) 284–299.CrossRefGoogle Scholar
  9. [9]
    C. T. Loy, K. Y. Lam and J. N. Reddy, Vibration of functionally graded cylindrical shells, International J. of Mechanical Sciences, 41 (3) (1999) 309–324.CrossRefzbMATHGoogle Scholar
  10. [10]
    M. C. Junger, Vibrations of elastic shell in a fluid medium and the associated radiation of sound, J. of Applied Mechanics, 19 (1952) 439–445.Google Scholar
  11. [11]
    X. M. Zhang, Frequency analysis of submerged cylindrical shells with the wave propagation approach, International J. of Mechanical Sciences, 44 (7) (2002) 1259–1273.CrossRefzbMATHGoogle Scholar
  12. [12]
    X. Zhu, W. B. Ye, T. Y. Li and C. Chen, The elastic critical pressure prediction of submerged cylindrical shell using wave propagation method, Ocean Engineering, 58 (2013) 22–26.CrossRefGoogle Scholar
  13. [13]
    T. Y. Li, G. J. Zhang, X. Zhu and L. Xiong, The prediction of the elastic critical load of submerged eccentric cylindrical shell based on vibro-acoustic model, Ocean Engineering, 108 (2015) 471–479.CrossRefGoogle Scholar
  14. [14]
    J. Yan, T. Y. Li, J. X. Liu and X. Zhu, Input power flow in a submerged infinite cylindrical shell with doubly periodic supports, Applied Acoustics, 69 (8) (2008) 681–690.CrossRefGoogle Scholar
  15. [15]
    A. Kumar, S. L. Das and P. Wahi, Effect of radial loads on the natural frequencies of thin-walled circular cylindrical shells, International J. of Mechanical Sciences, 122 (2017) 37–52.CrossRefGoogle Scholar
  16. [16]
    M. N. Naeem, M. Gamkhar, S. H. Arshad and A. G. Shah, Vibration analysis of submerged thin FGM cylindrical shells, J. of Mechanical Science and Technology, 27 (3) (2013) 649–656.CrossRefGoogle Scholar
  17. [17]
    H. Huang and Q. Han, Stability of pressure-loaded functionally graded cylindrical shells with inelastic material properties, Thin-Walled Structures, 92 (2015) 21–28.CrossRefGoogle Scholar
  18. [18]
    J. Jamali, M. H. Naei, F. Honarvar and M. Rajabi, Acoustic scattering from functionally graded cylindrical shells, Archives of Mechanics, 63 (1) (2011) 25–56.MathSciNetzbMATHGoogle Scholar
  19. [19]
    W. Flügge, Stresses in Shells, 2nd Ed., Springer-Verlag, New York (1973).CrossRefzbMATHGoogle Scholar
  20. [20]
    X. W. Liu, B. Liang and R. Li, Study on stability of functionally graded cylindrical shells subjected to hydrostatic pressure, Applied Mechanics and Materials, 580–583 (2014) 2920–2923.CrossRefGoogle Scholar
  21. [21]
    R. Li, B. Liang, N. A. Noda, W. Zhang and H. Y. Xu, Study on vibration of functionally graded cylindrical shells subjected to hydrostatic pressure by wave propagation method, Journal of Ship Mechanics, 17 (1–2) (2013) 148–154 (in Chinese).Google Scholar
  22. [22]
    P. M. Morse and K. U. Ingard, Theoretical Acoustics, McGraw-Hill, New York (1968).Google Scholar
  23. [23]
    R. H. Plaut and L. N. Virgin, Use of frequency data to predict buckling, J. of Engineering Mechanics, 116 (10) (1990) 2330–2335.CrossRefGoogle Scholar
  24. [24]
    P. Khazaeinejad, M. M. Najafizadeh, J. Jenabi and M. R. Isvandzibaei, On the buckling of functionally graded cylindrical shells under combined external pressure and axial compression, J. of Pressure Vessel Technology, 132 (6) (2010) 064501.CrossRefGoogle Scholar
  25. [25]
    Y. W. Kim, Temperature dependent vibration analysis of functionally graded rectangular plates, J. of Sound and Vibration, 284 (3–5) (2005) 531–549.CrossRefGoogle Scholar
  26. [26]
    S. C. Pradhan, C. T. Loy, K. Y. Lam and J. N. Reddy, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics, 61 (1) (2000) 111–129.CrossRefGoogle Scholar
  27. [27]
    W. B. Ning, J. G. Zhang and W. D. Chen, Dynamics and stability of a functionally graded cylindrical thin shell containing swirling annular fluid flow including initial axial loads, Acta Mechanica, 227 (8) (2016) 2157–2170.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    M. R. Isvandzibaei, H. Jamaluddin and R. I. Raja Hamzah, Analysis of the vibration behavior of FGM cylindrical shells including internal pressure and ring support effects based on Love-Kirchhoff theory with various boundary conditions, J.of Mechanical Science and Technology, 28 (7) (2014) 2759–2768.CrossRefzbMATHGoogle Scholar

Copyright information

© KSME & Springer 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringHenan University of Science and TechnologyLuoyangChina

Personalised recommendations