Coupled systems mechanics

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Vibration investigation of an imperfect FGM cylindrical shell reinforced by various types of stiffeners with temperature-dependent properties resting on an elastic foundation

  • Ahmed Muthanna (Department of Mechanical Engineering, College of Engineering, University of Anbar) ;
  • Mohammed Ali (Department of Medical Instruments Engineering Techniques, College of Engineering, University of Al Maarif) ;
  • Hamad M. Hasan (Department of Mechanical Engineering, College of Engineering, University of Anbar) ;
  • Khalid B. Najim (Department of Civil Engineering, College of Engineering, University of Anbar) ;
  • Emad Kadum Njim (Ministry of Industry and Minerals, State Company for Rubber and Tires Industries) ;
  • Royal Madan (Department of Mechanical Engineering, Graphic Era (Deemed to be University)) ;
  • Mohammed H. Al-Maamori (Prosthetics and Orthotics Engineering Department, College of Engineering, AL-Mustaqbal University)
  • Received : 2025.02.12
  • Accepted : 2025.04.11
  • Published : 2025.04.25
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Abstract

This study examines the vibration response of imperfect functionally graded (FG) cylindrical shells reinforced with different types of eccentrically placed stiffeners. The material composition follows a power-law distribution, varying with different grading indices. The analysis is conducted analytically under simply supported boundary conditions, considering longitudinal and transverse stiffeners of circular, rectangular, and triangular cross-sections. The cylindrical shell, resting on an elastic foundation, is subjected to thermo-mechanical loading. The governing equations are derived using the first-order shear deformation theory, incorporating von Kármán-Donnell nonlinear geometric formulation and the smeared stiffener method. A numerical approach combining the fourth-order Runge-Kutta method and Galerkin's procedure is employed to evaluate the dynamic response and natural frequencies. Results reveal that increasing foundation stiffness enhances natural frequencies by 15% and reduces vibration amplitude. Conversely, elevated temperature leads to a 12% reduction in natural frequencies and a decrease in structural rigidity, highlighting the coupled effects of thermal and mechanical loads on the shell's dynamic behavior.

Keywords

References

  1. Ali, A.Y. and Hasan, H.M. (2019), "Nonlinear dynamic stability of an imperfect shear deformable orthotropic functionally graded material toroidal shell segments under the longitudinal constant velocity", Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 233(19-20), 6827-6850. https://doi.org/10.1177/0954406219867991.
  2. Ali, A.Y. and Hasan, H.M. (2022), "Non-linear large amplitude vibration of orthotropic FGM convex and concave toroidal shell segments including the damping effect using the shear deformation theory", Thin Wall. Struct., 173, 109035. https://doi.org/10.1016/j.tws.2022.109035.
  3. Arefi, M., Karroubi, R. and Irani-Rahaghi, M. (2016), "Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer", Appl. Math. Mech., 37(7), 821-834. https://doi.org/10.1007/s10483-016-2098-9.
  4. Bayat, M., Sahari, B.B., Saleem, M., Ali, A. and Wong, S.V. (2009), "Bending analysis of a functionally graded rotating disk based on the first order shear deformation theory", Appl. Math. Model., 33(11), 4215-4230. https://doi.org/10.1016/j.apm.2009.03.001.
  5. Bich, D.H. and Long, V.D. (2007), "Non-linear dynamical analysis of laminated reinforced composite doubly curved shallow shells", Viet. J. Mech., 29(3), 257-269. https://doi.org/10.15625/0866-7136/29/3/5538.
  6. Bich, D.H., Dung, D.V. and Nam, V.H. (2012), "Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels", Compos. Struct., 94(8), 2465-2473. https://doi.org/10.1016/j.compstruct.2012.03.012.
  7. Chorfi, S.M. and Houmat, A. (2010), "Non-linear free vibration of a functionally graded doubly-curved shallow shell of elliptical plan-form", Compos. Struct., 92(10), 2573-2581. https://doi.org/10.1016/j.compstruct.2010.02.001.
  8. Daneshmand, S., Vini, M.H., Sajadi, S.M., Mouthanna, A., Jasim, D.J., Hammoodi, K.A., Hekmatifar, M. and Nasajpour-Esfahani, N. (2023), "Numerical and experimental investigations of mechanical, tribological, and electrical properties of laminated Bi-metal Al/SiC/Ni composites", Mater. Today Commun., 37, 107355. https://doi.org/10.1016/j.mtcomm.2023.107355.
  9. Deniz, A., Zerin, Z. and Karaca, Z. (2016), "Winkler-Pasternak foundation effect on the frequency parameter of FGM truncated conical shells in the framework of shear deformation theory", Compos. Part B: Eng., 104, 57-70. https://doi.org/10.1016/j.compositesb.2016.08.006.
  10. Duc, N.D. and Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations", Aerosp. Sci. Technol., 40, 115-127. https://doi.org/10.1016/j.ast.2014.11.005.
  11. Duc, N.D. and Tung, H.V. (2010), "Nonlinear analysis of stability for functionally graded cylindrical panels under axial compression", Fifth Conference of the Asian Consortium for Computational Materials Science ACCMS-5, Hanoi, Vietnam, September.
  12. Duc, N.D., Bich, D.H. and Cong, P.H. (2016), "Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations", J. Therm. Stress., 39(3), 278-297. https://doi.org/10.1080/01495739.2015.1125194
  13. Ellali, M., Amara, K. and Bouazza, M. (2024), "Thermal buckling of porous FGM plate integrated surface-bonded piezoelectric", Couple. Syst. Mech., 13(2), 171-186. https://doi.org/10.12989/csm.2024.13.2.171.
  14. Farhan, Z.A., Jweeg, M.J., Njim, E.K., Mouthanna, A., Mujtaba, A.F., Royal, M., Khobragade, P. and Kumar, R.P. (2025), "Nonlinear frequency and dynamic response of PLA polymeric imperfect FG sandwich plates under hygrothermal conditions", Couple. Syst. Mech., 14(1), 1-19. https://doi.org/10.12989/csm.2025.14.1.001.
  15. Gao, K., Gao, W., Wu, D. and Song, C. (2018), "Nonlinear dynamic stability of the orthotropic functionally graded cylindrical shell surrounded by Winkler-Pasternak elastic foundation subjected to a linearly increasing load", J. Sound Vib., 415, 147-168. https://doi.org/10.1016/j.jsv.2017.11.038.
  16. Hong Cong, P., Anh, V.M. and Dinh Duc, N. (2017), "Nonlinear dynamic response of eccentrically stiffened FGM plate using Reddy's TSDT in thermal environment", J. Therm. Stress., 40(6), 704-732. https://doi.org/10.1080/01495739.2016.1261614.
  17. Huy Bich, D., Dinh Duc, N. and Quoc Quan, T. (2014), "Nonlinear vibration of imperfect eccentrically stiffened functionally graded double curved shallow shells resting on elastic foundation using the first order shear deformation theory", Int. J. Mech. Sci., 80, 16-28. https://doi.org/10.1016/j.ijmecsci.2013.12.009.
  18. Kadum Njim, E., Al-Maamori, M.H., Madan, R., H Bakhy, S., Al-Waily, M., Khobragade, P. and Hadji, L. (2024), "Numerical and analytical investigation of free vibration behavior of porous functionally graded sandwich plates", Mech. Adv. Compos. Struct., https://doi.org/10.22075/macs.2024.34962.1710.
  19. Karamanlı, A. (2018), "Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory", Compos. Struct., 189, 127-136. https://doi.org/10.1016/j.compstruct.2018.01.060.
  20. Khayra, D., Meziane, M.A.A., Hadji, L., Atmane, H.A., Bennai, R. and Madan, R. (2024), "Effect of porosity and boundary conditions on dynamic characteristics of cracked plates made of functionally graded materials", Adv. Concrete Constr., 18(3), 175-190. https://doi.org/10.12989/acc.2024.18.3.175.
  21. Kiarasi, F., Babaei, M., Asemi, K., Dimitri, R. and Tornabene, F. (2022), "Free vibration analysis of thick annular functionally graded plate integrated with piezo-magneto-electro-elastic layers in a hygrothermal environment", Appl. Sci., 12(20), 10682. https://doi.org/10.3390/app122010682.
  22. Kumar, R., Miglani, A. and Kumar, R. (2024), "Axisymmetric deformation of thick circular plate in microelongated thermoelastic solid", Couple. Syst. Mech., 13(3), 231-245. https://doi.org/10.12989/csm.2024.13.3.231.
  23. Li, S.R., Fu, X.H. and Batra, R.C. (2010), "Free vibration of three-layer circular cylindrical shells with functionally graded middle layer", Mech. Res. Commun., 37(6), 577-580. https://doi.org/10.1016/j.mechrescom.2010.07.006.
  24. Madan, R. and Bhowmick, S. (2021), "A numerical solution to thermo‐mechanical behavior of temperature dependent rotating functionally graded annulus disks", Aircraft Eng. Aerosp. Technol., 93(4), 733-744. https://doi.org/10.1108/AEAT-01-2021-0012.
  25. Madan, R., Khobragade, P. and Bhowmick, S. (2024), "Impact of porosity on free vibration and limit analysis of power-law-based functionally graded disks", Multidis. Model. Mater. Struct., 20(6), 1192-1212. https://doi.org/10.1108/MMMS-04-2024-0108.
  26. Matsunaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2D higher-order deformation theory", Compos. Struct., 84(2), 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006.
  27. Mouthanna, A., Bakhy, S.H. and Al-Waily, M. (2023), "Analytical investigation of nonlinear free vibration of porous eccentrically stiffened functionally graded sandwich cylindrical shell panels", Iran. J. Sci. Technol., Trans. Mech. Eng., 47(3), 1035-1053. https://doi.org/10.1007/s40997-022-00555-4.
  28. Mouthanna, A., Hasan, H.M. and Najim, K.B. (2018), "Nonlinear vibration analysis of functionally graded imperfection of cylindrical panels reinforced with different types of stiffeners", 2018 11th International Conference on Developments in eSystems Engineering (DeSE), 284-289.
  29. Neamah, R.A., Nassar, A.A., Alansari, L.S., Njim, E.K. and Madan, R. (2025), "Experimental and analytical investigation of free vibration of a crack FG beam reinforced with alumina nano particles", Adv. Nano Res., 18(1), 19-31. https://doi.org/10.12989/anr.2025.18.1.019.
  30. Njim, E.K., Hasan, H.R., Jweeg, M.J., Al-Waily, M., Hameed, A.A., Youssef, A.M. and Elsayed, F.M. (2024), "Mechanical properties of sandwiched construction with composite and hybrid core structure", Adv. Polym. Technol., 2024(1), 3803199. https://doi.org/10.1155/2024/3803199.
  31. Njim, E.K., Jweeg, M.J., Al-Maamori, M.H., Idan, Z.S., Al‑Waily, M., Mouthanna, A. and Hadji, L. (2024), "Wear Behavior analysis of imperfect functionally graded parts: Analytical and experimental techniques", BIO Web Conf., 97, 00001. https://doi.org/10.1051/bioconf/20249700001.
  32. Quan, T.Q., Tran, P., Tuan, N.D. and Duc, N.D. (2015), "Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations", Compos. Struct., 126, 16-33. https://doi.org/10.1016/j.compstruct.2015.02.056.
  33. Raad, H., Najim, E., Jweeg, M., AlWaily, M., Hadji, L. and Madan, R. (2024), "Vibration analysis of sandwich plates with hybrid composite cores combining porous polymer and foam structures", Journal of Comput. Appl. Mech., 55(3), 485-499. https://doi.org/10.22059/jcamech.2024.377658.1121.
  34. Rajawat, A.S., Sharma, A.K. and Gehlot, P. (2018), "Free vibration analysis of Stiffened Laminated Plate using FEM", Mater. Today: Proce., 5(2), 5313-5321. https://doi.org/10.1016/j.matpr.2017.12.115.
  35. Singh, M., Saini, D.S., Matharu, S.P.S. and Salim, M. (2023), "Finite element analysis of alloy based hip implant under static loading conditions", Recent Advances in Material, Manufacturing, and Machine Learning, CRC Press.
  36. Singh, S.K., Sondhi, L., Sahu, R.K., Madan, R. and Yadav, S. (2024), "Investigating thermo-mechanical stresses in functionally graded disks using Navier's method for different loading conditions", Struct. Eng. Mech., 91(6), 627-642. https://doi.org/10.12989/sem.2024.91.6.627.
  37. Sofiyev, A.H. (2018), "Application of the first order shear deformation theory to the solution of free vibration problem for laminated conical shells", Compos. Struct., 188, 340-346. https://doi.org/10.1016/j.compstruct.2018.01.016.
  38. Taheran, F., Monfared, V., Daneshmand, S. and Abedi, E. (2016), "Nonlinear vibration analysis of directional drill string considering effect of drilling mud and weight on bit", J. Vibroeng., 18(2), 1280- 1287. https://doi.org/10.21595/jve.2015.16480.
  39. Tayeb, B., Abderezak, R. and Daouadji, T.H. (2024), "Mechanical behavior of composite beam aluminum sandwich honeycomb strengthened by imperfect FGM plate under thermo-mechanical loading", Couple. Syst. Mech., 13(2), 133-151. https://doi.org/10.12989/csm.2024.13.2.133.
  40. Vini, M.H. and Daneshmand, S. (2019), "Investigation of bonding properties of Al/Cu bimetallic laminates fabricated by the asymmetric roll bonding techniques", Adv. Comput. Des., 4(1), 33-41. https://doi.org/10.12989/acd.2019.4.1.033.
  41. Zohra, A., Rabia, B. and Tahar, H.D. (2024), "Study and analysis of porosity distribution effects on the buckling behavior of functionally graded plates subjected to diverse thermal loading'', Couple. Svst. Mech., 13(2), 115-132. https://doi.org/10.12989/csm.2024.13.2.115.
  42. Zouatnia, N., Hadji, L., Atmane, H.A., Nebab, M., Madan, R., Bennai, R. and Dahmane, M. (2024), "Analysis of free vibration in bi-directional power law-based FG beams employing RSD theory", Couple. Syst. Mech., 13(4), 359-373. https://doi.org/10.12989/csm.2024.13.4.359.