Vibration Analysis of a Thin-Walled Cylindrical Shell Containing Fluid under Dynamic Loading

Authors

  • Nader Salmani Khas Department of Civil Engineering, Shahid Beheshti University, Tehran, Iran.
  • Khadijeh Ghaziyani * Department of mathematics, Lahijan Azad University, Lahijan, Iran. https://orcid.org/0000-0001-7860-3010

https://doi.org/10.48314/ijrceai.v3i2.59

Abstract

Liquid-filled cylindrical tanks are extensively used in industrial facilities, including petroleum, chemical, water supply, and nuclear power systems. These structures are frequently subjected to dynamic excitations caused by earthquakes, impact loads, and operational vibrations, which significantly influence their structural integrity and serviceability. The interaction between the contained liquid and the flexible tank wall alters the dynamic characteristics of the system by introducing additional inertia and fluid–structure coupling effects. Therefore, accurate prediction of the natural frequencies of partially filled tanks is essential for safe and reliable structural design. This study presents a dynamic free vibration analysis of a partially filled thin-walled cylindrical shell with one end fixed and the other end free. The fluid is assumed to be incompressible, inviscid, and irrotational, while the shell behavior is modeled according to thin shell theory. The governing equations are derived using the Rayleigh–Ritz energy method combined with Lagrange's equations. The fluid contribution is incorporated through the added-mass formulation obtained from the solution of the Laplace equation for the fluid domain. Numerical simulations are performed for both steel and concrete cylindrical tanks considering different liquid height ratios and shell geometric parameters. The results demonstrate that the natural frequencies increase as the liquid filling height decreases. Furthermore, increasing the shell height-to-radius ratio also leads to higher natural frequencies for both the first and second vibration modes. The proposed formulation provides an efficient analytical framework for evaluating the dynamic characteristics of liquid-filled cylindrical tanks and can serve as a practical tool for preliminary structural design and vibration assessment.  

Keywords:

Fluid–structure interaction, Thin cylindrical shell, Free vibration, Rayleigh–Ritz method, Added mass, Natural frequency

References

  1. [1] Soedel, W. (2004). Vibrations of shells and plates. Taylor & Francis Group. https://doi.org/10.4324/9780203026304
  2. [2] Rotter, J. M. (2017). Shell buckling transformed: Mechanics, design processes and their inter-relation. Stahlbau, 86(4), 315–324. https://doi.org/10.1002/stab.201710478
  3. [3] Reddy, J. N. (2006). Theory and analysis of elastic plates and shells. Taylor & Francis Group. https://doi.org/10.1201/9780849384165
  4. [4] Lu, S., Wang, W., Chen, W., Ma, J., Shi, Y., & Xu, C. (2019). Behaviors of thin-walled cylindrical shell storage tank under blast impacts. Shock and vibration, 2019(1), 6515462. https://doi.org/10.1155/2019/6515462
  5. [5] Al-Yacouby, A. M., Hao, L. J., Liew, M. S., Ratnayake, R. M. C., & Samarakoon, S. M. K. (2021). Thin-walled cylindrical shell storage tank under blast impacts: Finite element analysis. Materials, 14(22), 1–24. https://doi.org/10.3390/ma14227100
  6. [6] Feng, J., Wu, Y., Xue, J., & Lin, J. (2024). Dynamic stability analysis of laminated cylindrical shells considering fluid–structure interaction. Composite structures, 340, 118183. https://doi.org/10.1016/j.compstruct.2024.118183
  7. [7] Ohayon, R., & Soize, C. (1998). Structural acoustics and vibration. Academic Press. https://doi.org/10.1016/B978-0-12-524945-4.X5000-2
  8. [8] Morand, H. J. P., & Ohayon, R. (1995). Fluid-structure interaction: Applied numerical methods. Wiley. https://www.wiley.com/en-us/shop/general-introductory-mechanical-engineering/fluid-structure-interaction-applied-numerical-methods-p-9780471944591
  9. [9] Love, A. E. H. (2013). A treatise on the mathematical theory of elasticity. Cambridge University Press. https://www.cambridge.org/ir/universitypress/subjects/mathematics/historical-mathematical-texts/treatise-mathematical-theory-elasticity-4th-edition
  10. [10] Calladine, C. R. (1983). Theory of shell structures. Cambridge University Press. https://books.google.com/books?id=REKJpbYCtu4C
  11. [11] Amabili, M. (2018). Nonlinear mechanics of shells and plates in composite, soft and biological materials. Cambridge University Press. https://doi.org/10.1017/9781316422892
  12. [12] Li, Y. Z., Fu, J. W., Qian, L. F., & Wang, H. Y. (2023). On the discussions of nonlinear terms in the large deformation model of thin-walled cylindrical shells. Mechanics of solids, 58(4), 1214–1227. https://doi.org/10.3103/S0025654423600216
  13. [13] Lee, H., & Kwak, M. K. (2017). Free vibration analysis of a circular cylindrical shell using the Rayleigh-Ritz method and comparison of different shell theories. Journal of sound and vibration, 353, 385–397. https://doi.org/10.1016/j.jsv.2017.03.042
  14. [14] Amabili, M. (1999). Vibrations of circular tubes and shells filled and partially immersed in dense fluids. Journal of sound and vibration, 221(4), 567–585. https://doi.org/10.1006/jsvi.1998.2050
  15. [15] Gonçalves, P. B., & Batista, R. C. (1987). Frequency response of cylindrical shells partially submerged or filled with liquid. Journal of sound and vibration, 113(1), 59–70. https://doi.org/10.1016/S0022-460X(87)81340-8
  16. [16] Amabili, M. (2000). Vibrations of fluid-filled hermetic cans. Journal of fluids and structures, 14(2), 235–255. https://doi.org/10.1006/jfls.1999.0267
  17. [17] Kim, Y. W., Lee, Y. S., & Ko, S. H. (2004). Coupled vibration of partially fluid-filled cylindrical shells with ring stiffeners. Journal of sound and vibration, 276(3), 869–897. https://doi.org/10.1016/j.jsv.2003.08.008
  18. [18] Tănase, M. (2024). A comprehensive synthesis on analytical algorithms for assessing elastic buckling loads of thin-walled isotropic and laminated cylindrical shells. Processes, 12(10), 1–27. https://doi.org/10.3390/pr12102120
  19. [19] Ibrahim, R. A. (2005). Liquid sloshing dynamics: Theory and applications. Cambridge University Press. https://books.google.com/books?id=ctvhvH74ZzEC
  20. [20] Yamaki, N. (1984). Elastic stability of circular cylindrical shells. Elsevier.
  21. [21] Chen, J. Y., Zhou, H. S., Xiao, Y. H., Wang, X. W., & Zhang, Z. (2026). Analytical and numerical analyses of thin-walled cylindrical structures in multifactorial stabilities. International journal of mechanics and materials in design, 22(1), 62. https://doi.org/10.1007/s10999-026-09888-3

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Published

2026-06-22

Issue

Vol. 3 No. 2 (2026): International Journal of Researches on Civil Engineering with Artificial Intelligence (IJRCEAI)

Section

Articles

How to Cite

Salmani Khas, N., & Ghaziyani, K. (2026). Vibration Analysis of a Thin-Walled Cylindrical Shell Containing Fluid under Dynamic Loading. International Journal of Researches on Civil Engineering With Artificial Intelligence , 3(2), 155-166. https://doi.org/10.48314/ijrceai.v3i2.59

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