Effect of Hydrostatic Pressure on the Free Vibrations of Hybrid Cylindrical Shell

Document Type : Solid Mechanics

Authors

1 M.Sc Student, Faculty of Graduate Studies, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

2 Corresponding author: Assistant Professor, Faculty of Graduate Studies, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

3 Associate Professor, Faculty of Graduate Studies, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

Abstract

Considering the increasing use of hybrid cylindrical shells in various industries, the free vibration analysis of these types of structures is very important. In this research, the free vibrations of the hybrid cylindrical shell under the influence of hydrostatic pressure have been analyzed and investigated. Investigating the hydrostatic pressure in hybrid shells is one of the important and required things for the optimal design of the structure, investigating the performance of the structure in different environmental conditions, bearing and resistance to pressure, etc. The boundary conditions for the cylindrical shell have been considered as fixed, free and simple, the equations governing the structure of the hybrid cylindrical shell are based on the displacement field and the stress and strain relations in matrix form using the first-order shear deformation theory of the shell and Hamilton's principle obtained and using generalized differential quadratic numerical method, the governing equations of the structure were solved and the effect of fiber angle, composite materials, hydrostatic pressure, composite to metal ratio, length to radius and thickness to radius of the cylinder on the natural frequency of the shell was investigated  and analyzed. Numerical results have been compared and validated with the results of the research. The results show that the hybrid shell with the distribution of composite materials and in a specific volume ratio shows better behavior against different hydrostatic pressure.

Highlights

  • Increasing hydrostatic pressure decreases the natural frequency.
  • Effect of composite material on natural frequency of hybrid cylindrical shell.
  • Generalized Differential Quadrature method

Keywords

Main Subjects

References

[1] Reddy JN and Liu CF. A higher-order shear deformation theory of laminated elastic shells. International journal Engineering and Science. 1985; 23(3): 319–330. DOI :10.1016/0020 7225(85)90051-5.
 [2] Rand O and Stavsky Y. Response and eigenfrequencies of rotating composite cylindrical shells.  journal Sound and Vibration. 1996; 192(1): 65–77. DOI :10.1006/jsvi.1996.0176.
[3] Lam KY and Loy CT. Influence of boundary conditions for a thin laminated rotating cylindrical shell. Composite Structures. 1998; 41(3–4): 215–228. DOI :10.1016/S0263-8223(98)00012-9.
[4] Lee YS and Kim YW. Effect of boundary conditions on natural frequencies for rotating composite cylindrical shells with orthogonal stiffeners. Advances in Engineering Software. 1999; 30(9–11): 649–655. DOI :10.1016/S0965-9978(98)00115-X.
[5] Suzuki K, Shikanai G and Chino T. Vibrations of composite circular cylindrical vessels. International journal of Solids and Structures. 1998; 35(22): 2877–2899. DOI :10.1016/S0020-7683(97)00356-9.
[6] Ng TY, Li H and Lam KY. Generalized differential quadrature for free vibration of rotating composite laminated conical shell with various boundary conditions. International journal of Mechanical Sciences. 2003; 45(3): 567–587. DOI :10.1016/S0020-7403(03)00042-0.
[7] Jafari AA and Bagheri M. Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution.  Journal Sound and Vibration. 2006. 296(1–2): 353–367. DOI :10.1016/j.jsv.2006.03.001.
[8] Golfman Y and Sudbury MA. Dynamic stability of the lattice structures in the manufacturing of carbon fiber epoxy/composites including the influence of damping properties. Journal of Advanced Materials. 2007; 3:11-20.
[9] Khalili SMR, Davar A and Malekzadeh Fard K. Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory. International journal of Mechanical Sciences. 2012; 56(1): 1–25. DOI :10.1016/j.ijmecsci.2011.11.002.
[10] Zhao L and Wu J. Natural frequency and vibration modal analysis of composite laminated plate. Advanced Materials Research. 2013: 711:  396–400. DOI :10.4028/www.scientific.net/AMR.711.396.
[11] Hemmatnezhad M, Rahimi GH and Ansari R. On the free vibrations of grid-stiffened composite cylindrical shells. Acta Mechanica. 2014; 225(2): 609–623. DOI :10.1007/s00707-013-0976-1.
[12] Tullu A, Ku TW and Kang BS. Elastic deformation of fiber-reinforced multi-layered composite conical shell of variable stiffness. Composite Structures. 2016; 154: 634–645. DOI :10.1016/j.compstruct.2016.07.064.
[13] Zarei M and Rahimi GH. Free vibration analysis of grid stiffened composite conical shells. Journal of Science and Technology of Composites. 2017; 4(1):1–8.
[14] Shen HS, Xiang Y, Fan Y and Hui D. Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments. Composites Part B: Engineering. 2018; 136: 177–186. DOI :10.1016/j.compositesb.2017.10.032.
[15] Qin Z, Yang Z, Zu J and Chu F. Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates. International journal of Mechanical Sciences. 2018; 142–143: 127–139. DOI :10.1016/j.ijmecsci.2018.04.044.
[16] Lopatin A. Buckling of composite cylindrical shells with rigid end disks under hydrostatic pressure‏. ‏Composite Structures. 2017; 173: 136-143. DOI :10.1016/j.compstruct.2017.03.109.
[17] Kiani Y, Dimitri R and Tornabene F. Free vibration study of composite conical panels reinforced with FG-CNTs. Engineering Structures. 2018; 172: 472–482. DOI :10.1016/j.engstruct.2018.06.006.
[18] Shen KC and Pan G. Buckling and strain response of filament winding composite cylindrical shell subjected to hydrostatic pressure: numerical solution and experiment. Composite Structures. 2021; 276(2):114534. DOI :10.1016/j.compstruct.2021.114534.
[19] Shahgholian DS, Rahimi G, Zarei M and Salehipour H. Free vibration analyses of composite sandwich cylindrical shells with grid cores: experimental study and numerical simulation. Mechanics Based Design of Structures and Machines.2022; 50(2): 687–706. DOI :10.1080/15397734.2020.1725565.
[20] Wu JH, Liu RJ, Duan Y and Sun YD. Free and forced vibration of fluid-filled laminated cylindrical shell under hydrostatic pressure‏. International Journal of Pressure Vessels and Piping. 2023; 202:104925. DOI :10.1016/j.ijpvp.2023.104925.
[21] Cho JR. Free vibration analysis of functionally graded porous cylindrical panels reinforced with graphene platelets. Nanomaterials. 2023; 13(9): 1441. DOI :10.3390/NANO13091441.
[22] Coskun T, Sahin OS. Modal and random vibration responses of composite overwrapped pressure vessels with various geodesic dome trajectories. Journal of Reinforced Plastics and Composites. 2024; 21:07316844241241567. DOI :10.1177/07316844241241567.
[23] Meng S, Zhong R, Wang Q, Shi X, Qin B. Vibration characteristic analysis of three-dimensional sandwich cylindrical shell based on the Spectro-Geometric method. Composite Structures. 2024; 327:117661. DOI :10.1016/j.compstruct.2023.117661.
[24] Wang RT and Lin ZX. Vibration analysis of ring-stiffened cross-ply laminated cylindrical shells. Journal of Sound and Vibration. 2006; 295(3–5): 964–987. DOI :10.1016/j.jsv.2006.01.061.
[25] Rao SS. Vibration of continuous systems. John Wiley & Sons, INC. 2007.
[26] Donnell LH. Stability of thin-walled tubes under torsion. Transactions of the American Society of Mechanical Engineers. 1934 Feb 1;56(2):108. DOI :10.1115/1.4019670.
[27] Amabili M. Nonlinear vibrations and stability of shells and plates. 2008; ISBN:9780521883.
[28] Bochkarev SA and Matveenko VP. Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid. Computers & Structures. 2011; 89(7–8): 571–580. DOI :10.1016/j.compstruc.2010.12.016.
[29] Sun Z, Hu G, Nie X, Sun J. An analytical symplectic method for buckling of ring-stiffened graphene platelet-reinforced composite cylindrical shells subjected to hydrostatic pressure. Journal of Marine Science and Engineering. 2022;10(12):1834. DOI :10.3390/jmse10121834.
[30] Bellman R and Casti J. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications. 1971; 34(2): 235–238. DOI :10.1016/0022-247X(71)90110-7.
[31] Shu C. Differential quadrature and its application in engineering. Springer London. 2000.
[32] Shu C and Du H. Free vibration analysis of laminated composite cylindrical shells by DQM. Composites Part B: Engineering. 1997; 28(3): 267–274. DOI :10.1016/S1359-8368(96)00052-2.
[33] Chung H. Free vibration analysis of circular cylindrical shells. Journal of sound and Vibration. 1981; 74(3): 331–350. DOI :10.1016/0022-460X(81)90303-5.
[34] Arshad S, Naeem MN, Sultana N, Shah AG and Iqbal ASZ. Vibration analysis of bi-layered FGM cylindrical shells‏. Archive of Applied Mechanics 2011;81:319-43. DOI :10.1007/s00419-010-0409-8.
[35] Wang Y and Wu D. Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory. Aerospace Science and Technology. 2017; 66: 83–91. DOI :10.1016/J.AST.2017.03.003.
[36] Loy CT, Lam KY and Shu C. Analysis of cylindrical shells using generalized differential quadrature. Shock and Vibration. 1997; 4(3): 193–198. DOI :10.3233/SAV-1997-4305.
 
Aerospace Mechanics
Volume 20, Issue 2 - Serial Number 76
Serial No. 76, Summer
July 2024
Pages 87-103

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History

  • Receive Date: 29 February 2024
  • Revise Date: 17 March 2025
  • Accept Date: 11 May 2024
  • Publish Date: 21 June 2024

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