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Vibration analysis and optimization of functionally graded carbon nanotube reinforced doubly-curved shallow shells

  • Hammou, Zakia (Physical chemistry Department, Chemistry Faculty, University of Science and Technology of Oran, USTO) ;
  • Guezzen, Zakia (Composite Structures and Innovative Materials Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, USTO) ;
  • Zradni, Fatima Z. (Oorganic Synthesis, Physico-chemistry, Biomolecular and Environment Laboratory, Chemical Engineering Department, Chemistry Faculty, University of Science and Technology of Oran, USTO) ;
  • Sereir, Zouaoui (Composite Structures and Innovative Materials Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, USTO) ;
  • Tounsi, Abdelouahed (YFL (Yonsei Frontier Lab), Yonsei University) ;
  • Hammou, Yamna (Maritime Sciences and Engineering Laboratory, Mechanical Engineering Faculty, University of Science and Technology of Oran, USTO)
  • Received : 2021.08.12
  • Accepted : 2022.07.04
  • Published : 2022.07.25
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Abstract

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.

Keywords

Acknowledgement

The authors would like to acknowledge financial support from the Algerian Ministry for Higher Education and Scientific Research (MESRS), especially the General Directorate of Scientific Research and Technological Development (DGRSDT).

References

  1. Ahmadi, H., Bayat, A. and Duc, N. D (2021). "Nonlinear forced vibrations analysis of imperfect stiffened FG doubly curved shallow shell in thermal environment using multiple scales method", Compos. Struct., 256, 113090. https://doi.org/10.1016/j.compstruct.2020.113090.
  2. Alhazza, K.A (2002), "Nonlinear vibrations of doubly curved cross-ply shallow shells", Ph.D. Dissertation, Virginia Polytechnic Institute and State University, Balcksburg.
  3. Alijani, F.,Amabili, M., Karagiozis, K. and Bakhtiari-Nejad, F. (2011a), "Nonlinear vibrations of functionally graded doubly curved shallow shells", J. Sound Vib., 330(7), 1432-1454. https://doi.org/10.1016/j.jsv.2010.10.003.
  4. Alijani, F., Amabili M. and Bakhtiari-Nejad, F. (2011b), "On the accuracy of the multiple scales method for non-linear vibrations of doubly curved shallow shells", J. Non Linear Mech., 46(1), 170-179. https://doi.org/10.1016/j.ijnonlinmec.2010.08.006.
  5. Amabili, M., Pellicano, F., Paidoussis, MP. (1998), "Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid", J. Fluids. Struct., 12(7), 883-918. https://doi.org/10.1006/jfls.1998.0173.
  6. Bogdanovich, A. (1991), Non-Linear Dynamic Problems for Composite Cylindrical Shells, Elsevier Applied Science, New York, USA.
  7. Chen, J.C., Babcock, C.D. (1975) "Non-linear vibration of cylindrical shells", AIAA J., 13, 868-876. https://doi.org/10.2514/3.60462.
  8. 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.
  9. Civalek, O. and Avcar, M. (2022) "Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. Comput., 38, 489-521. https://doi.org/10.1007/s00366-020-01168-8.
  10. Dindarloo, M.H. and Li, L. (2019), "Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory", Composites Part B, 175, 107170. https://doi.org/10.1016/j.compositesb.2019.107170.
  11. Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment", European J. Mech. / A Solids, 75, 355-366. https://doi.org/10.1016/j.euromechsol.2019.01.024.
  12. El-Ashmawy, A.M., Xu, Y. and El-Mahdy, L.A. (2021), "Mechanical properties improvement of bi-directional functionally graded laminated MWCNT reinforced composite beams using an integrated tailoring-optimization approach", Microporous Mesoporous Mater., 314, 110875. https://doi.org/10.1016/j.micromeso.2021.110875.
  13. Eyvaziana, A., Shahsavari, D. and Karami, B. (2020), "On the dynamic of graphene reinforced nanocomposite cylindrical shells subjected to a moving harmonic load", J. Eng. Sci., 154, 103339. https://doi.org/10.1016/j.ijengsci.2020.103339.
  14. Farrokhian, A. and Kolahchi, R. (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.
  15. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  16. Karami, B., Gheisari, P., Reza Nazemosadat, S.M, Akbari, P., Shahsavari, D., Naghizadeh, M. (2020), "Elastic wave characteristics of graphene nanoplatelets reinforced composite nanoplates", Struct. Eng. Mech., 74(6), 809-819. https://doi.org/10.12989/sem.2020.74.6.809.
  17. Khazaei, P., Mohammadimehr, M., (2020), "Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FGSWCNTs based on a nonlocal strain gradient theory", Comput. Concr. 26(1), 31-52. https://doi.org/10.12989/cac.2020.26.1.031.
  18. Khosravi, F., Simyari, M., Hosseini, S.A., Tounsi, A. (2020), "Size dependent axial free and forced vibration of carbon nanotube via different rod models", Adv. Nano Res., 9(3), 157-172. https://doi.org/10.12989/anr.2020.9.3.157.
  19. Liu, Y., Qin, Z. and Chu, F. (2021a), "Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads", Int. J. Mech. Sci., 201, 106474. https://doi:10.1016/j.ijmecsci.2021.106474.
  20. Liu, Y., Qin, Z. and Chu, F. (2021b), "Nonlinear dynamic responses of sandwich functionally graded porous cylindrical shells embedded in elastic media under1:1 internal resonance", Appl. Math. Mech. -Engl. Ed., 42(6), 805-818. https://doi.org/10.1007/s10483-021-2740-7.
  21. Liu, Y., Qin, Z. and Chu, F. (2021c), "Nonlinear forced vibrations of FGM sandwich cylindrical shells with porosities on an elastic substrate", Nonlinear Dyn., 104(2), 1007-1021. https://doi:10.1007/s11071-021-06358-7.
  22. Madenci, E. (2021), "Free vibration and static analyses of metalceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. http://dx.doi.org/10.12989/scs.2021.39.5.493.
  23. Mahesh,V. and Harursampath, D. (2022) "Nonlinear vibration of functionally graded magneto-electro-elastic higher order plates reinforced by CNTs using FEM", Eng. Comput., 38, 1029-1051. https://doi.org/10.1007/s00366-020-01098-5.
  24. Matsunaga, H. (2008), "Free vibration and stability of functionally graded shallow shells according to a 2D higher-order deformation theory", Compos. Struct., 84, 132-146. https://doi.org/10.1016/j.compstruct.2007.07.006.
  25. Mohammadi, F. and Sedaghati, R. (2012), "Vibration analysis and design optimization of viscoelastic sandwich cylindrical shell", J. Sound Vib., 331(12), 2729-2752. https://doi.org/10.1016/j.jsv.2012.02.004.
  26. Nayfeh, A. H. (1981), Introduction to Perturbation Techniques, Wiley, New Jersey, USA.
  27. Qin, Z., Pang, X., Safaei, B. and Chu, F. (2019c), "Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions", Compos. Struct., 220, 847-860. http://dx.doi.org/10.1016/j.compstruct.2019.04.046.
  28. Qin, Z., Safaei, B., Pang, X. and Chu, F. (2019a), "Traveling wave analysis of rotating functionally graded graphene platelet reinforced nanocomposite cylindrical shells with general boundary conditions", Results Phys., 15, 102752. https://doi.org/10.1016/j.rinp.2019.102752.
  29. Qin, Z., zhao, S., pang, X., safaei, B. and Chu, F. (2019b), "A unified solution for vibration analysis of laminated functionally graded shallow shells reinforced by graphene with general boundary conditions", Int. J. Mech. Sci., 170, 105341. https://doi.org/10.1016/j.ijmecsci.2019.10534.
  30. Rasool M.D., Mehrdad F. and Aminallah P. (2013), "Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method", Mater. Design, 44, 256-266. https://doi.org/10.1016/j.matdes.2012.07.069.
  31. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, CRS Press, Boca Raton, USA.
  32. Rostami, R. and Mohammadi, M. (2022) "Vibration control of rotating sandwich cylindrical shell-reinforced nanocomposite face sheet and porous core integrated with functionally graded magneto-electro-elastic layers", Eng. Comput., 38, 87-100. https://doi.org/10.1007/s00366-020-01052-5.
  33. Sahu, N.K., Biswal, D.K., Joseph, S.V. and Mohanty, S.C. (2020), "Vibration and damping analysis of doubly curved viscoelastic-FGM sandwich shell structures using FOSDT", Structures, 26, 24-38. https://doi.org/10.1016/j.istruc.2020.04.007.
  34. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube reinforced composite plates in thermal environments", Compos Struct, 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  35. Shen, H.S. and Xiang, Y. (2012), "Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments", Comput. Methods Appl. Mech. Eng., 213, 196-205. http://dx.doi.org/10.1016/j.cma.2011.11.025.
  36. Shen, H-S. and Xiang, Y. (2014), "Nonlinear vibration of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments", Compos. Struct., 111, 291-300. https://doi.org/10.1016/j.compstruct.2014.01.010.
  37. Shi, J.X., Nagano, T. and Shimoda, M. (2017), "Fundamental frequency maximization of orthotropic shells using a free-form optimization method", Compos. Struct., 170, 135-145. https://doi.org/10.1016/j.compstruct.2017.03.007.
  38. Shimoda, M. and Lui, Y. (2016), "Node-based free-form optimization method for vibration problems of shell structures", Comput. Struct., 177, 91-102. https://doi.org/10.1016/j.compstruc.2016.08.011.
  39. Song, Z.G., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments", Int. J. Mech. Sci, 115-116, 339-347. http://dx.doi.org/10.1016/j.ijmecsci.2016.06.020.
  40. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623.
  41. Vishesh, R.K. and Subrata, K.P. (2015) "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. http://dx.doi.org/10.12989/scs.2015.18.3.693.
  42. Vuong, P.M. and Duc, N.D. (2018), "Nonlinear response and buckling analysis of eccentrically stiffened FGM toroidal shell segments in thermal environment", Aerosp. Sci. Technol., 79, 383-398. https://doi.org/10.1016/j.ast.2018.05.058
  43. Wu, H., Kitipornchai, S. and Yang, J. (2018), "Free vibration of thermo-electro-mechanically post buckled FG-CNTRC beams with geometric imperfections", Steel Compos. Struct., 29(3), 319-332. https://doi.org/10.12989/scs.2018.29.3.319.
  44. Wu, Z., Zhang, Y. and Yao, G. (2020), "Nonlinear forced vibration of functionally graded carbon nanotube reinforced composite circular cylindrical shells", Acta Mech, 231(6), 2497-2519. http://dx.doi.org/10.1007/s00707-020-02650-6.
  45. Xiang, R., Panb, Z.Z., Ouyangc, H. and Zhanga, L.W. (2020), "A study of the vibration and lay-up optimization of rotating crossply laminated nanocomposite blades", Compos. Struct., 235, 111775. https://doi.org/10.1016/j.compstruct.2019.111775.
  46. Zhang, L.W., Song, Z.G., Qiao, P., Liew and K.M. (2017), "Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads", Comput. Methods Appl. Mech. Eng, 313, 889-903. https://doi.org/10.1016/j.cma.2016.10.020.