Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear resonance and chaos in rotating functionally graded carbon nanotube-reinforced composite annular plates

  • G.L. She (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • J.Q. Xu (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2025.02.07
  • Accepted : 2025.05.02
  • Published : 2025.03.25
⟨ Previous Next ⟩

Abstract

This article investigates the nonlinear forced vibration behavior of a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rotating annular plate subjected to external excitation forces. First, the governing equations are established based on the first-order shear deformation theory (FSDT) and the Hamiltonian principle. Subsequently, the Galerkin method is utilized to discretize the nonlinear equations. Considering pinned and fixed boundary conditions, the multi-scale method is used to derive analytical solutions. By comparing the results with existing literature, good consistency is achieved, validating the accuracy of the research. Finally, the influences of different parameters on the nonlinear vibration of the annular plate are analyzed. The results indicate that temperature, distribution patterns and volume fraction of CNTs, rotational velocity, and geometric configurations of the plate significantly affect the resonance position. Additionally, the damping coefficient and external load exhibit a pronounced impact on the resonance domain but do not affect the natural frequency. As external excitation varies, periodic motion and chaotic phenomena are observed in the system.

Keywords

References

  1. Abdelrahman, A.A., Shanab, R.A., Esen, I. and Eltaher, M.A. (2022), "Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory", Steel Compos. Struct., 44(2), 241-256. https://doi.org/10.12989/scs.2022.44.2.241.
  2. Alazwari, M.A., Daikh, A.A. and Eltaher, M.A. (2022), "Novel quasi 3D theory for mechanical responses of FG-CNTs reinforced composite nanoplates", Adv. Nano. Res., 12(2), 117-137. https://doi.org/10.12989/anr.2022.12.2.117.
  3. Assie, A.E. (2024), "Nonlinear bending analysis of bidirectional graded porous plates with elastic foundations relative to neutral surface", Adv. Aircraft Spacecraft Sci., 11(2), 129-152. https://doi.org/10.12989/aas.2024.11.2.129.
  4. Babaei, H. (2022), "Thermomechanical analysis of snap-buckling phenomenon in long FG-CNTRC cylindrical panels resting on nonlinear elastic foundation", Compos. Struct., 286, 115199. https://doi.org/10.1016/j.compstruct.2022.115199.
  5. Baferani, A.H. and Ohadi, A.R. (2022), "Effect of in-plane loads on the natural frequencies of transversely isotropic thick annular sector plates resting on elastic foundation", Proc. Inst. Mech. Eng. Part C-J. Mech. Eng. Sci., 236(14), 8057-8072. https://doi.org/10.1177/09544062221084191.
  6. Cai, Y. and She, G.L. (2025), "Nonlinear dynamic response of magneto-electro-elastic cylindrical shells subjected to moving load", Mech. Adv. Mater. Struct., 1-12. https://doi.org/10.1080/15376494.2025.2463090.
  7. Cuong-Le, Thanh., Tran, L.V., Vu-Huu, T., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019), "Sizedependent nonlinear analysis and damping responses of FG-CNTRC micro-plates", Comput. Meth. Appl. Mech. Eng., 353, 253-276. https://doi.org/10.1016/j.cma.2019.05.002.
  8. Dastjerdi, S., Alibakhshi, A., Akgoz, B. and Civalek, O. (2023a), "On a comprehensive analysis for mechanical problems of spherical structures", Int. J. Eng. Sci., 183, 103796. https://doi.org/10.1016/j.ijengsci.2022.103796.
  9. Dastjerdi, S., Civalek, O., Malikan, M. and Akgoz, B. (2023b), "On analysis of nanocomposite conical structures", Int. J. Eng. Sci., 191, 103918. https://doi.org/10.1016/j.ijengsci.2023.103918.
  10. Dastjerdi, S., Malikan, M., Eremeyev, V.A., Akgoz, B. and Civalek, O. (2021a), "On the generalized model of shell structures with functional cross-sections", Compos. Struct., 272, 114192. https://doi.org/10.1016/j.compstruct.2021.114192.
  11. Dastjerdi, S., Naeijian, F., Akgoz, B. and Civalek, O. (2021b), "On the mechanical analysis of microcrystalline cellulose sheets", Int. J. Eng. Sci., 166, 103500. https://doi.org/10.1016/j.ijengsci.2021.103500.
  12. Dat, N.D., Thanh, N.V., MinhAnh, V. and Duc, N.D. (2022), "Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer", Mech. Adv. Mater. Struct., 29(10), 1431-1448. https://doi.org/10.1080/15376494.2020.1822476.
  13. Djilali, N., Bousahla, A.A., Kaci, A., Selim, M.M., Bourada, F., Tounsi, A., Tounsi, A., Benrahou, K.H. and Mahmoud, S.R. (2022), "Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT", Steel Compos. Struct., 42(6), 779-789. https://doi.org/10.12989/scs.2022.42.6.779.
  14. Fan, Y.H. and She, G.L. (2025) "Nonlinear transient response of graphene platelets reinforced metal foams beam considering initial geometrical imperfection and viscoelastic elastic foundation", Comput. Concrete, 35(1), 59-70. https://doi.org/10.12989/cac.2025.35.1.059.
  15. Fan, Y.H., She, G.L. and Li, C. (2025), "Nonlinear transient response analysis of revolution doubly curved shells", Arch. Civil Mech. Eng., 25, 145. https://doi.org/10.1007/s43452-025-01187-6.
  16. Foroutan, K. and Dai, L. (2024). "Nonlinear free and forced vibrations of oblique stiffened porous FG shallow shells embedded in a nonlinear elastic foundation", Struct. Eng. Mech., 89(1), 33-46. https://doi.org/10.12989/sem.2024.89.1.033.
  17. Gan, L.L. and She, G.L. (2025a), "Nonlinear combined resonance of magneto-electro-elastic plates", Eur. J. Mech.-A/Solid., 109, 105492. https://doi.org/10.1016/j.euromechsol.2024.105492.
  18. Gan, L.L. and She, G.L. (2025b), "Nonlinear transient responses of FG-CNTRC cylindrical shells: Influence of hygro-thermal effect", Comput. Concrete, 35(5), 557-567. https://doi.org/10.12989/cac.2025.35.5.557.
  19. Guo, X.Y., Zhang, Y.M., Luo, Z. and Cao, D.X. (2023), "Nonlinear dynamics analysis of a graphene laminated composite plate based on an extended Rayleigh-Ritz method", Thin Wall. Struct., 186, 110673. https://doi.org/10.1016/j.tws.2023.110673.
  20. Hebali, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Hussain, M. and Tounsi, A. (2022), "Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model", Geomech. Eng., 28(1), 49-64. https://doi.org/10.12989/gae.2022.28.1.049.
  21. Hu, Y.D. and Xu, H.R. (2022), "Nonaxisymmetric magnetoelastic coupling natural vibration analysis of annular plates in an induced nonuniform magnetic field", Nonlin. Dyn., 109(2), 657-687. https://doi.org/10.1007/s11071-022-07475-7.
  22. Huang, X.H., Yang, J., Wang, X.E. and Azim, I. (2022), "Combined analytical and numerical approach for auxetic FG-CNTRC plate subjected to a sudden load", Eng. Comput., 38, 55-70. https://doi.org/10.1007/s00366-020-01106-8.
  23. Li, W.Q., Hu, Y.D. and Li, Z. (2023), "Magneto-aero-elastic superharmonic and subharmonic resonances, bifurcations and chaos of conductive spinning circular plates", Int. J. Bifurc. Chaos, 33(01), 2330001. https://doi.org/10.1142/S021812742330001X.
  24. Li, Y.P. and She, G.L. (2025a), "Nonlinear dynamic response of porous graphene platelets reinforced plates subjected to moving load considering initial geometrical imperfection", J. Vib. Eng. Technol., 13(1), 17. https://doi.org/10.1007/s42417-024-01651-2.
  25. Li, Y.P. and She, G.L. (2025b), "Nonlinear dynamic response of graphene platelets reinforced cylindrical shells under moving loads considering initial geometric imperfection", Eng. Struct., 323(A), 119241. https://doi.org/10.1016/j.engstruct.2024.119241.
  26. Liu, Z.F., Wu, X.Y., Yu, M. and Habibi, M. (2022), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings", Mech. Bas. Des. Struct. Mach., 50(11), 3722-3746. https://doi.org/10.1080/15397734.2020.1815544.
  27. Ma, L.H., Liu, X.L. and Moradi, Z. (2022), "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 38(3), 2583-2607. https://doi.org/10.1007/s00366-020-01210-9.
  28. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022a), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math., 10(4), 583. https://doi.org/10.3390/math10040583,2022.
  29. Melaibari, A., Daikh, A.A., Basha, M., Wagih, A., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022b), "A dynamic analysis of randomly oriented functionally graded carbon nanotubes/fiber-reinforced composite laminated shells with different geometries", Math., 10(3), 408. https://doi.org/10.3390/math10030408.
  30. Noroozi, M. and Bakhtiari-Nejad, F. (2021), "Nonlinear vibration of a nanocomposite laminated piezoelectric trapezoidal actuator in subsonic airflow under combined electrical and forcing excitations", Proc. Inst. Mech. Eng. Part C-J. Mech. Eng., 235(2), 4784-4817. https://doi.org/10.1177/0954406220911075.
  31. She, G.L. and He, Y.J. (2025), "Nonlinear thermal buckling of magneto-electro-thermal-elastic plates with geometric imperfection", Struct. Eng. Mech., 93(2), 115-123. https://doi.org/10.12989/sem.2025.93.2.115.
  32. She, G.L., Gan, L.L. and Xu, J.Q. (2025a), "Nonlinear snap-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Geomech. Eng., 40(3), 183-191. https://doi.org/10.12989/gae.2025.40.3.183.
  33. She, G.L., Ma, Z.S., Li, C. and Eltaher, M.A. (2025b), "Geometrically nonlinear transient response of graphene platelets reinforced metal foams arbitrary quadrilateral plates under blast load", Thin Wall. Struct., 210, 113018. https://doi.org/10.1016/j.tws.2025.113018.
  34. Shen, Z.Q., Xia, J. and Cheng, P. (2019), "Geometrically nonlinear dynamic analysis of FG-CNTRC plates subjected to blast loads using the weak form quadrature element method", Compos. Struct., 209, 775-788. https://doi.org/10.1016/j.compstruct.2018.11.009.
  35. Thanh, N.V., Khoa, N.D., Tuan, N.D., Tran, P. and Duc, N.D. (2017), "Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations", J. Therm. Stress., 40(10), 1254-1274. https://doi.org/10.1080/01495739.2017.1338928.
  36. Tornabene, F., Viola, E. and Inman, D.J. (2009), "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures", J. Sound Vib., 328(3), 259- 290. https://doi.org/10.1016/j.jsv.2009.07.031.
  37. Valizadeh, R. and Eipakchi, H. (2022), "Effect of transverse and radial deformations on nonlinear frequencies of annular plates: Perturbation approach", Ship. Offsh. Struct., 17(9), 2058-2069. https://doi.org/10.1080/17445302.2021.1979720.
  38. Wu, H.L., Zhu, J., Kitipornchai, S., Wang, Q., Ke, L.L. and Yang J. (2020), "Large amplitude vibration of functionally graded graphene nanocomposite annular plates in thermal environments", Compos. Struct., 239, 112047. https://doi.org/10.1016/j.compstruct.2020.112047.
  39. Xu, H.R., Hu, Y.D. and Hao, Y. (2022), "Magnetoelastic nonlinear free vibration of an annular plate under a nonuniform magnetic field of the long straight current-carrying wire", Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 102(6), e202000299. https://doi.org/10.1002/zamm.202000299.
  40. Xu, J.Q., Li, Y.P. and She, G.L. (2025), "Nonlinear low-velocity impact response of GPLRMF doubly curved shells in thermal environment", Comput. Concrete, 35(3), 219-229. https://doi.org/10.12989/cac.2025.35.3.219.
  41. Yang, Y., Li, J., Chen, B., Dong, Y. and Li, Y. (2023), "Symmetric and asymmetric vibrations of rotating GPLRC annular plate", Int. J. Mech. Sci., 250, 108282. https://doi.org/10.1016/j.ijmecsci.2023.108282.
  42. Zhai, Y.C., Yu, X., Yue, X.J., Wang, P.H. and Zhang, P. (2021), "Dynamic property of functionally graded carbon nanotube-reinforced composite plates with viscoelastic core", Compos. Struct., 275, 114466. https://doi.org/10.1016/j.compstruct.2021.114466.
  43. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023), "Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection", Aerosp. Sci. Technol., 142, 108693. https://doi.org/10.1016/j.ast.2023.108693.
  44. Zhou, Z.W., Chen, M.X., Xiong, Y.P., Jia, W.C., Dong, W.K. and Xie, K. (2021), "Experimental and mixed analytical-numerical studies for free and forced vibrations of Z-reinforced sandwich plates stiffened by steel ribs", Compos. Struct., 272, 114221. https://doi.org/10.1016/j.compstruct.2021.114221.