Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear harmonic resonances of spinning graphene platelets reinforced metal foams cylindrical shell with initial geometric imperfections in thermal environment

  • Yi-Wen Zhang (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2023.06.01
  • Accepted : 2023.11.06
  • Published : 2023.12.10
⟨ Previous Next ⟩

Abstract

This paper reveals theoretical research to the nonlinear dynamic response and initial geometric imperfections sensitivity of the spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shell under different boundary conditions in thermal environment. For the theoretical research, with the framework of von-Karman geometric nonlinearity, the GPLRMF cylindrical shell model which involves Coriolis acceleration and centrifugal acceleration caused by spinning motion is assumed to undergo large deformations. The coupled governing equations of motion are deduced using Euler-Lagrange principle and then solved by a combination of Galerkin's technique and modified Lindstedt Poincare (MLP) model. Furthermore, the impacts of a set of parameters including spinning velocity, initial geometric imperfections, temperature variation, weight fraction of GPLs, GPLs distribution pattern, porosity distribution pattern, porosity coefficient and external excitation amplitude on the nonlinear harmonic resonances of the spinning GPLRMF cylindrical shells are presented.

Keywords

References

  1. Ahmadi, H., Bayat, A. and Duc, N.D. (2020), "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. Allam, M.N.M., Radwan, A.F. and Sobhy, M. (2021), "Hygrothermal deformation of spinning FG graphene sandwich cylindrical shells having an auxetic core", Eng. Struct., 251, 113433. https://doi.org/10.1016/j.engstruct.2021.113433.
  3. Chai, Q.D. and Wang, Y.Q. (2021), "Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion", Eng. Struct., 252, 113718. https://doi.org/10.1016/j.engstruct.2021.113718.
  4. Chai, Q.D., Wang, Y.Q. and Teng, M.W. (2022a), "Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions", Appl. Math. Mech-Engl., 43(8), 1203-1218. https://doi.org/10.1007/s10483-022-2892-7.
  5. Chai, Q.D., Wang, Y.Q. and Yang, F.L. (2022b), "Frequency response of spinning cylindrical shells with discontinuous conditions: A semi method", Thin Wall. Struct., 182, 110253. https://doi.org/10.1016/j.tws.2022.110253.
  6. Chen, S.H. and Cheung, Y.K. (1996), "A modified Lindstedt-Poincare method for a strongly nonlinear system with quadratic and cubic nonlinearities", Shock Vib., 3, 279-285. https://doi.org/10.1155/1996/231241.
  7. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus, 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0.
  8. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  9. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civil Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  10. Ding, H.X. and She, G.L. (2023b), "Nonlinear primary resonance behavior of graphene platelets reinforced metal foams conical shells under axial motion", Nonlin. Dyn., 111(15), 13723-13752. https://doi.org/10.1007/s11071-023-08564-x.
  11. Ding, H.X. and She, G.L. (2023c), "Nonlinear combined resonances of axially moving graphene platelets reinforced metal foams cylindrical shells under forced vibrations", Nonlinear Dyn., https://doi.org/10.1007/s11071-023-09059-5.
  12. Ding, H.X., Eltaher, M.A. and She, G.L. (2023a), "Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections", Aerosp. Sci. Technol., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435.
  13. Ding, H.X., Liu, H.B., She, G.L. and Wu, F. (2023c), "Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory", Comput. Concrete, 32(2), 207-215. https://doi.org/10.12989/cac.2023.32.2.207.
  14. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  15. Ding, H.X., Zhang, Y.W. and She, G.L. (2023b), "Propagation characteristics of guided waves in CNTRCs plates resting on elastic foundations in a thermal environment", Wave. Random Complex Media, 1-18. https://doi.org/10.1080/17455030.2023.2235611.
  16. Dong, Y.H., He, L.W., Wang, L., Li, Y.H. and Yang, J. (2018a), "Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: Analytical study", Aerosp. Sci. Tech., 82-83, 466-478. https://doi.org/10.1016/j.ast.2018.09.037.
  17. Dong, Y.H., Li, X.Y., Gao, K., Li, Y.H. and Yang, J. (2022), "Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: Effects of spinning motion and thermal environment", Nonlin. Dyn., 99(2), 981-1000. https://doi.org/10.1007/s11071-019-05297-8.
  18. Dong, Y.H., Li, X.Y., Gao, K., Li, Y.H. and Yang, J. (2019), "Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment", Nonlin. Dyn., 99(2), 981-1000. https://doi.org/10.1007/s11071-019-05297-8.
  19. Dong, Y.H., Zhu, B., Wang, Y., He, L.W., Li, Y.H. and Yang, J. (2019), "Analytical prediction of the impact response of graphene reinforced spinning cylindrical shells under axial and thermal loads", Appl. Math. Model., 71, 331-348. https://doi.org/10.1016/j.apm.2019.02.024.
  20. Dong, Y.H., Zhu, B., Wang, Y., Li, Y.H. and Yang, J. (2018b), "Nonlinear free vibration of graded graphene reinforced cylindrical shells: Effects of spinning motion and axial load", J. Sound Vib., 437, 79-96. https://doi.org/10.1016/j.jsv.2018.08.036.
  21. Fan, L.Y., Kong, D.G., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022), "Optimization dynamic responses of laminated multiphase shell in thermo-electro-mechanical conditions", Adv. Nano. Res., 13(1), 29-45. https://doi.org/10.12989/anr.2022.13.1.029.
  22. Gan, L.L. and She, G.L. (2024), "Nonlinear low-velocity impact of magneto-electro-elastic plates with initial geometric imperfection", Acta Astronautica, 214, 11-29. https://doi.org/10.1016/j.actaastro.2023.10.016.
  23. Gan, L.L., Xu, J.Q. and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Struct. Eng. Mech., 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645.
  24. Gu, X.J., Hao, Y.X. Zhang, W., Liu, L.T. and Chen, J. (2018), "Free vibration of rotating cantilever pre-twisted panel with initial exponential function type geometric imperfection", Appl. Math. Model., 68, 327-352. https://doi.org/10.1016/j.apm.2018.11.037.
  25. Guo, D., Zheng, Z.C. and Chu, F.L. (2002), "Vibration analysis of spinning cylindrical shells by finite element method", Int. J. Solid. Struct., 39(3), 725-739. https://doi.org/10.1016/S0020-7683(01)00031-2.
  26. Halpin, J.C. and Kardos, J.L. (1976), "The Halpin-Tsai equations: A review", Polym. Eng. Sci., 16, 344-352. https://doi.org/10.1002/pen.760160512.
  27. Hao, Y.X., Wang, M.X., Zhang, W., Liu, L.T. and Yang, S.W. (2021), "Natural vibration of imperfect sandwich plates considering the effects of transverse stretching", J. Vib. Control, 28, 2467-2482. https://doi.org/10.1177/10775463211013153.
  28. Heidari-Soureshjani, A., Talebitooti, M., Pakravan, I. and Talebitooti, R. (2022), "Critical speed and frequency behavior of rotating joined FG-CNTRC conical-conical shells", Eng. Struct., 266, 114508. https://doi.org/10.1016/j.engstruct.2022.114508.
  29. Jafari, A.A. and Bagheri, M. (2006), "Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution", J. Sound Vib., 296, 353-367. https://doi.org/10.1016/j.jsv.2006.03.001.
  30. Jia, J.F., Lai, A.D., Qu, J.L., Zhao, J.Y., Sun, J.B., Zhou, Z.H., Xu, X.S. and Lim, C.W. (2021), "Effects of local thinning defects and stepped thickness for free vibration of cylindrical shells using a symplectic exact solution approach", Acta Astronautica, 178, 658-671. https://doi.org/10.1016/j.actaastro.2020.09.046.
  31. Jiao, J., Xu, J., Yuan, X.G. and Chen, L.Q. (2022), "Axisymmetric 3: 1 internal resonance of thin-walled hyperelastic cylindrical shells under both axial and radial excitations", Acta Mechanica Sinica, 38(8), 521417. https://doi.org/10.1007/s10409-022-09006-x.
  32. Ke, L.L., Yang, J. and Kitipornchai, S. (2010), "Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams", Compos. Struct., 92, 676-683. https://doi.org/10.1016/j.compstruct.2009.09.024.
  33. Li, J., Xue, Y. and Li, F. (2023a), "Active band gap control of magnetorheological meta-plate using frequency feedback control law", J. Sound Vib., 567, 118076. https://doi.org/10.1016/j.jsv.2023.118076
  34. Li, W., Hao, Y.X., Zhang, W. and Yang, H. (2020), "Resonance response of clamped functionally graded cylindrical shells with initial imperfection in thermal environments", Compos. Struct., 259, 113245. https://doi.org/10.1016/j.compstruct.2020.113245.
  35. Li, X., Chen, X.C. and Jiang, W. (2022a), "Dynamic stability of graded graphene reinforced truncated conical shells under both periodic spinning speeds and axial loads considering thermal effects", Eng. Struct., 256, 113963. https://doi.org/10.1016/j.engstruct.2022.113963.
  36. Li, X., Zhang, X.L. and Zhou, Z.H. (2022b), "Free vibration analysis of a spinning composite laminated truncated conical shell under hygrothermal environment", Symmetry-Basel, 14(7), 1369. https://doi.org/10.3390/sym14071369.
  37. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel Compos. Struct., 46(5), 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  38. Li, Z.C., Zheng, J.X. and Zhang, Z. (2020), "Thermal nonlinear performance of the porous metal cylinders with composite graphene nanofiller reinforcement encased in elastic mediums", Int. J. Mech. Sci., 181, 105698. https://doi.org/10.1016/j.ijmecsci.2020.105698.
  39. Liang, K. and Wang, Z.H. (2022), "Imperfection sensitivity study of the thermal-mechanical buckling of laminated composite cylinders using a novel reduced-order modeling method", Thin Wall. Struct., 182, 110224. https://doi.org/10.1016/j.tws.2022.110224.
  40. Liang, K. and Zhou, Z.T. (2022), "Nonlinear static behavior of three-layer annular plates reinforced with nanoparticles", Acta Astronautica, 193, 444-453. https://doi.org/10.1016/j.actaastro.2022.01.009.
  41. Liew, K.M., Ng, T.Y., Zhao, X., Reddy, J.N. (2002), "Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells", Comput. Meth. Appl. Mech. Eng., 191(37-38), 4141-4157. https://doi.org/10.1007/s11071-019-05297-8.
  42. Lin, B.C., Zhu, B., Chen, B., Han, J. and Li, Y.H. (2022), "Nonlinear primary resonance behaviors of rotating FGCNTRC beams with geometric imperfections", Aerosp. Sci. Tech., 121, 107333. https://doi.org/10.1016/j.ast.2022.107333.
  43. Lin, G.J., Li, F., Zhang, Q.T., Chen, P.W., Sun, W.F., Saikov, I., Shcherbakov, V. and Alymov, M. (2021), "Dynamic instability of fiber composite cylindrical shell with metal liner subjected to internal pulse loading", Compos. Struct., 280, 114906. https://doi.org/10.1016/j.compstruct.2021.114906.
  44. Liu, H., Dong, Y.H., Wang, L.F. and Hu, H.Y. (2022), "Travelling-modes of a spinning cylindrical shell with elastic boundaries", Int. J. Mech. Sci., 238, 107844. https://doi.org/10.1016/j.ijmecsci.2022.107844.
  45. Liu, S.H., Yu, J.K., Ali, H.E. and Al-Masoudy, M.M. (2022), "Homotopic analysis for post-buckling of cylindrical shells with local thickness defects", Adv. Nano. Res., 13(5), 427-435. https://doi.org/10.12989/anr.2022.13.5.427.
  46. Liu, Y.Q. and Chu, F.L. (2012), "Nonlinear vibrations of rotating thin circular cylindrical shell", Nonlin. Dyn., 67(2), 1467-1479. https://doi.org/10.1007/s11071-011-0082-7.
  47. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  48. Mahmoudkhani, S. and Laghaie, K.S. (2022), "Flutter analysis of sandwich panel with the constrained viscoelastic layer considering the effects of the imperfection and the core thickness deformation", Thin Wall. Struct., 173, 108980. https://doi.org/10.1016/j.tws.2022.108980.
  49. Majidi-Mozafari, K., Bahaadini, R. and Saidi, A.R. (2021), "Aeroelastic flutter analysis of functionally graded spinning cylindrical shells reinforced with graphene nanoplatelets in supersonic flow", Mater. Res. Expr., 8(11), 115012. https://doi.org/10.1088/2053-1591/ac2ce4.
  50. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahma, A. and Eltaher, M.A. (2022), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math., 10(4), 583. https://doi.org/10.3390/math10040583.
  51. Mohamadi, A., Ghasemi, F.A. and Shahgholi, M. (2021), "Nonlinear vibration, stability, and bifurcation analysis of axially moving and spinning cylindrical shells", Mech. Bas. Des. Struct. Mach., 51(7), 4032-4062. https://doi.org/10.1080/15397734.2021.1949345.
  52. Parvez, M.T. and Khan, A.H. (2022), "Influence of geometric imperfections on the nonlinear forced vibration characteristics and stability of laminated angle-ply composite conical shells", Compos. Struct., 291, 115555. https://doi.org/10.1016/j.compstruct.2022.115555.
  53. Peng, X.B., Xu, J., Cheng, Y., Li, Y.H. and Yang, J. (2021), "The effect of curing deformation on the vibration behavior of laminated composite beams", Compos. Struct., 277, 114642. https://doi.org/10.1016/j.compstruct.2021.114642.
  54. Rafiee, M., Nitzsche, F. and Labrosse, M. (2016), "Rotating nanocomposite thin-walled beams undergoing large deformation", Compos. Struct., 150, 191-199. https://doi.org/10.1016/j.compstruct.2016.05.014.
  55. Raju, K.K. and Rao, G.V. (1976), "Large amplitude asymmetric vibrations of some thin shells of revolution", J. Sound Vib., 44(3), 327-333. https://doi.org/10.1016/S0022-460X(78)800236.
  56. Rodrigues, L., Silva, F.M.A. and Goncalves, P.B. (2020), "Influence of initial geometric imperfections on the 1:1:1:1 internal resonances and nonlinear vibrations of thin-walled cylindrical shells", Thin Wall. Struct., 151, 106730. https://doi.org/10.1016/j.tws.2020.106730.
  57. Safarpour, H., Pourghader, J. and Habibi, M. (2019), "Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator", J. Vib. Control, 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465.
  58. Salehi, M., Gholami, R. and Ansari, R. (2022), "Nonlinear resonance of functionally graded porous circular cylindrical shells reinforced by graphene platelet with initial imperfections using Higher-Order Shear Deformation theory", Int. J. Struct. Stab. Dyn., 22(06), 2250075. https://doi.org/10.1142/S0219455422500754.
  59. Shahgholian-Ghahfarokhi, D., Safarpour, M. and Rahimi, A. (2019), "Torsional buckling analyses of functionally graded porous nanocomposite cylindrical shells reinforced with graphene platelets (GPLs)", Mech. Bas. Des. Struct., 49(1), 102. https://doi.org/10.1080/15397734.2019.1666723.
  60. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stress., 44(10), 1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  61. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mechanica Sinica, 39, 522392. https://doi.org/10.1007/s10409-022-22392-x
  62. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  63. Sobhy, M. and Radwan, A.F. (2022), "An axial magnetic field effect on frequency analysis of rotating sandwich cylindrical shells with FG Graphene/AL face sheets and honeycomb core", Int. J. Appl. Mech., 14(08), 2250074. https://doi.org/10.1142/S1758825122500740.
  64. Song, J.P. and She, G.L. (2023), "Nonlinear resonance of axially moving GPLRMF plates with different boundary conditions", Struct. Eng. Sci., 86(3), 361-371. https://doi.org/10.12989/sem.2023.86.3.361.
  65. Sun, J.L., Jin, D.P. and Hu, H.Y. (2022), "Deployment dynamics and topology optimization of a spinning inflatable structure", Acta Mechanica Sinica, 38(10), 122100. https://doi.org/10.1007/s10409-022-22100-x.
  66. Villoria, R.G. and Miravete, A. (2007), "Mechanical model to evaluate the effect of the dispersion in nanocomposites", Acta Materialia, 55, 3025-3031. https://doi.org/10.1016/j.actamat.2007.01.007.
  67. Wang, B., Hao, P., Li, G., Zhang, J.X., Du, K.F., Tian, K., Wang, X.J. and Tang, X.H. (2014), "Optimum design of hierarchical stiffened shells for low imperfection sensitivity", Acta Mechanica Sinica, 30(3), 391-402. https://doi.org/10.1007/s10409-014-0003-3.
  68. Wang, G.D. and Yuan, H.Q. (2021), "Stability and critical spinning speed of a flexible liquid-filled rotor in thermal environment with nonlinear variable-temperature", Appl. Math. Model., 95, 143-158. https://doi.org/10.1016/j.apm.2021.01.056.
  69. Wang, Y. and Zhang, W. (2022), "On the thermal buckling and post-buckling responses of temperature-dependent graphene platelets reinforced porous nanocomposite beams", Compos. Struct., 296, 115880. https://doi.org//10.1016/j.compstruct.2022.115880.
  70. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Tech., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  71. Wang, Y.W. and Chen, J. (2022), "Nonlinear free vibration of rotating functionally graded graphene platelets reinforced blades with variable cross-sections", Eng. Anal. Bound Elem., 144, 262-278. https://doi.org/10.1016/j.enganabound.2022.08.032.
  72. Wu, F. and She, G.L. (2023), "Wave propagation in double nanobeams in thermal environments using the Reddy's high-order shear deformation theory", Adv. Nano Res., 14(6), 495-506. https://doi.org/10.12989/anr.2023.14.6.495.
  73. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  74. Xu, J.Q. and She, G.L. (2023a), "Thermal post-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Struct. Eng. Mech., 87(1), 85-94. https://doi.org/10.12989/sem.2023.87.1.085.
  75. Xu, J.Q. and She, G.L. (2023b), "The effects of temperature and porosity on resonance behavior of graphene platelet reinforced metal foams doubly-curved shells with geometric imperfection", Geomech. Eng., 35(1), 81-93. https://doi.org/10.12989/gae.2023.35.1.081.
  76. Xu, J.Q., She, G.L., Li. Y.P. and Gan, L.L. (2023), "Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection", Steel Compos. Struct., 47(6), 795-811. https://doi.org/10.12989/scs.2023.47.6.795.
  77. Xue, Y., Li, J., Wang, Y., Song, Z. and Krushynska, A.O. (2023), "Widely tunable magnetorheological metamaterials with nonlinear amplification mechanism", Int. J. Mech. Sci., 19, 108830. https://doi.org/10.1016/j.ijmecsci.2023.108830.
  78. Zhang, H.Y., Bai, H.F. and Zuo, Z.Y. (2020), "Nonlinear stability of natural-fiber-reinforced composite cylindrical shells with initial geometric imperfection considering moisture absorption and hygrothermal aging", Mater., 15(19), 6917. https://doi.org/10.3390/ma15196917.
  79. Zhang, W., Guo, L.J., Wang, Y.W., Mao, J.J. and Yan, J.W. (2022), "Nonlinear low velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads", Nonlin. Dyn., 110(4), 3255-3272. https://doi.org/10.1007/s11071-022-07809-5.
  80. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos, Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  81. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlin. Dyn., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  82. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2023.2180556
  83. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stress., 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  84. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  85. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023d), "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.
  86. Zhang, Y.W., She, G.L., Gan, L.L. and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  87. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  88. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  89. Zhao, T.Y., Yan, K., Li, H.W. and Wang, X. (2022b), "Study on theoretical modeling and vibration performance of an assembled cylindrical shell-plate structure with whirl motion", Appl. Math. Model., 110, 618-632. https://doi.org/10.1016/j.apm.2022.06.019.
  90. Zheng, Y.X., Jin, H.W. and Jiang, C.Y. (2022), "Assessment of nonlinear stability of geometrically imperfect beam based on numerical method", Adv. Nano Res., 13(2), 113-120. https://doi.org/10.12989/anr.2022.13.2.113.