DOI QR코드

DOI QR Code

Nonlinear forced vibration of axially moving functionally graded cylindrical shells under hygro-thermal loads

  • Jin-Peng Song (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yu-Jie He (College of Mechanical and Vehicle Engineering, Chongqing University)
  • 투고 : 2023.03.07
  • 심사 : 2023.12.05
  • 발행 : 2024.01.25

초록

Studying the dynamic behavior of axially moving cylindrical shells in hygro-thermal environments has important theoretical and engineering value for aircraft design. Therefore, in this paper, considering hygro-thermal effect, the nonlinear forced vibration of an axially moving cylindrical shell made of functionally graded materials (FGM) is studied. It is assumed that the material properties vary continuously along the thickness and contain pores. The Donnell thin shell theory is used to derive the motion equations of FGM cylindrical shells with hygro-thermal loads. Under the four sides clamped (CCCC) boundary conditions, the Gallekin method and multi-scale method are used for nonlinear analysis. The effects of power law index, porosity coefficient, temperature rise, moisture concentration, axial velocity, prestress, damping and external excitation amplitude on nonlinear forced vibration are explored through parametric research. It can be found that, the changes in temperature and humidity have a significant effect. Increasing in temperature and humidity will cause the resonance position to shift to the left and increase the resonance amplitude.

키워드

참고문헌

  1. Abazid, M.A., Zenkour, A.M. and Sobhy, M. (2020), "Wave propagation in FG porous GPLs-reinforced nanoplates under in-plane mechanical load and Lorentz magnetic force via a new quasi 3D plate theory", Mech. Based. Des. Struc., 50(5), 1831-1850. https://doi.org/10.1080/15397734.2020.1769651.
  2. Al Mukahal, F.H.H. and Sobhy, M. (2021), "Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM", Arch. Civ. Mech. Eng., 22(1), 12. https://doi.org/10.1007/s43452-021-00322-3
  3. Ali, S. and Hawwa, M.A. (2023), "Dynamics of axially moving beams: A finite difference approach", Ain Shams Eng. J., 14(1), 101817. https://doi.org/10.1016/j.asej.2022.101817.
  4. Akbas, S.D. (2019), "Hygro-thermal nonlinear analysis of a functionally graded beam", J. Appl. Comput. Merch., 5(2), 477-485. https://doi.org/10.22055/jacm.2018.26819.1360.
  5. Barati, M.R. and Zenkour, A.M. (2018), "Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions", J. Vib. Control, 24(10), 1910-1926. https://doi.org/10.1177/1077546316672788.
  6. Belalia, S.A. (2019), "Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates", J. Sandw. Struct. Mater., 21(3), 895-916. https://doi.org/10.1177/1099636217701299.
  7. Belarouci, A. and Fekrar, A. (2021), "A new quasi-3D theory for the study of the bending of thick FGM's plates on elastic foundation", Smart Struct. Syst., 27(5), 847-860. https://doi.org/10.12989/sss.2021.27.5.847.
  8. Beli, D., Rosa, M.I.N., De Marqui, C. and Ruzzene, M. (2022), "Wave beaming and diffraction in quasicrystalline elastic metamaterial plates", Phys. Rev. Res., 4(4), 043030. https://doi.org/10.1103/PhysRevResearch.4.043030.
  9. Belkhodja, Y., Ouinas, D., Fekirini, H., Vina Olay, J.A., Achour, B., Touahmia, M. and Boukendakdji, M. (2022), "A new hybrid HSDT for bending, free vibration, and buckling analysis of FGM plates (2D & quasi-3D)", Smart Struct. Syst., 29(3), 395-420. https://doi.org/10.12989/sss.2022.29.3.395.
  10. 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.
  11. 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.
  12. Chen, Y., Dong, S., Zang, Z., Gao, M., Zhang, J., Ao, C. and Zhang, Q. (2021), "Free transverse vibrational analysis of axially functionally graded tapered beams via the variational iteration approach", J. Vib. Control, 27(11-12), 1265-1280. https://doi.org/10.1177/1077546320940181.
  13. Cheng, Y., Wu, Y. and Guo, B.Z. (2021), "Boundary stability criterion for a nonlinear axially moving beam", Ieee T Automat. Contr., 67(11), 5714-5729. https://doi.org/10.1109/TAC.2021.3124754.
  14. Daikh, A.A., Drai, A., Bensaid, I., Houari, M.S.A. and Tounsi, A. (2021), "On vibration of functionally graded sandwich nanoplates in the thermal environment", J. Sandw. Struct. Mater., 23(6), 2217-2244. https://doi.org/10.1177/1099636220909790.
  15. Daikh, A.A., Houari, M.S.A. and Eltaher, M.A. (2021a), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347.
  16. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021b), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11(7), 3250. https://doi.org/10.3390/app11073250.
  17. Dastjerdi, S., Akgoz, B., Civalek, O., Malikan, M. and Eremeyev, V. A. (2020), "On the non-linear dynamics of torus-shaped and cylindrical shell structures", Int. J. Eng. Sci., 156, 103371. https://doi.org/10.1016/j.ijengsci.2020.103371.
  18. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  19. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Arch. Civ. Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  20. Ding, H.X. and She, G.L. (2023b), "Nonlinear primary resonance behavior of graphene platelets reinforced metal foams conical shells under axial motion", Nonlinear Dynam., 111(15), 13723-13752. https://doi.org/10.1007/s11071-023-08564-x.
  21. 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 Dynam., https://doi.org/10.1007/s11071-023-09059-5.
  22. 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.
  23. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  24. 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.
  25. 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, https://doi.org/10.1080/17455030.2023.2235611.
  26. 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.
  27. Ding, H.X., Zhang, Y.W., Li, Y.P. and She, G.L. (2023d), "Nonlinear low-velocity impact response of graphene platelets reinforced metal foams doubly curved shells", Steel Compos. Struct., 49(3), 281-291. https://doi.org/10.12989/scs.2023.49.3.281
  28. Dong, Y., Hu, H., Wang, L. and Mao, X. (2024), "Nonlinear coupled multi-mode vibrations of simply-supported cylindrical shells: Comparison studies", Commun. Nonlinear Sci. Numer. Simul., 128, 107667. https://doi.org/10.1016/j.cnsns.2023.107667.
  29. Ebrahimi, F., Karimiasl, M. and Selvamani, R. (2020). "Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading", Adv. Nano Res., 8(3), 203-214. https://doi.org/10.12989/anr.2020.8.3.203.
  30. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. with Comput., 38(4), 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  31. Esen, I., Daikh, A.A. and Eltaher, M.A. (2022b), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136(4),1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7.
  32. Fasihi, A., Shahgholi, M., Kudra, G. and Awrejcewicz, J. (2022), "Static and dynamic bifurcations analysis of a fluid-conveying pipe with axially moving supports surrounded by an external fluid", Int. J. Struct. Stab. Dy., 2350054. https://doi.org/10.1142/S0219455423500542.
  33. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541.
  34. 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.
  35. 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.
  36. Hadji, L. and Tounsi, A. (2021), "Static deflections and stress distribution of functionally graded sandwich plates with porosity", Smart Struct. Syst., 28(3), 343-354. https://doi.org/10.12989/sss.2021.28.3.343.
  37. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.
  38. Hashemi-Nejad, H., Saidi, A.R. and Bahaadini, R. (2022), "Wave propagation in rotating thin-walled porous blades reinforced with graphene platelets", Zamm-Z. Angew. Math. Me., 102(9), e202100502. https://doi.org/10.1002/zamm.202100502.
  39. Hirano, Y. (1988), "Nonlinear vibrations of composite material shells", University of Delaware.
  40. Huang, X.L. and Shen, H.S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41(9-10), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012.
  41. Karimiasl, M., Ebrahimi, F. and Akgoz, B. (2019), "Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading", Compos. Struct., 223, 110988. https://doi.org/10.1016/j.compstruct.2019.110988.
  42. Lal, A. and Markad, K. (2021), "Probabilistic-based nonlinear progressive failure analysis of piezoelectric laminated composite shell panels in hygrothermal environment", J. Aerosp. Eng., 34(6), 04021099. https://doi.org/10.1061/(ASCE)AS.1943-5525.0001345.
  43. 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.
  44. Li, Y. and Tang, Y. (2022), "Application of Galerkin iterative technique to nonlinear bending response of three-directional functionally graded slender beams subjected to hygro-thermal loads", Compos. Struct., 290, 115481. https://doi.org/10.1016/j.compstruct.2022.115481.
  45. Liu, Y. (2022), "Nonlinear dynamic analysis of an axially moving composite laminated cantilever beam", J. Vib. Eng. Technol., 1-13. https://doi.org/10.1007/s42417-022-00750-2.
  46. Liu, Z., Wu, X., Yu, M. and Habibi, M. (2022), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings", Mech. Based Des. Struc., 50(11), 3722-3746. https://doi.org/10.1080/15397734.2020.1815544.
  47. Loy, C.T., Lam, K.Y. and Shu, C. (1997), "Analysis of cylindrical shells using generalized differential quadrature", Shock Vib., 4(3), 193-198. https://doi.org/10.1155/1997/538754.
  48. Luo, Y. and Zhang, D. (2022), "Dynamic analysis of an axially moving underwater pipe conveying pulsating fluid", Front. Mar. Sci., 1981. https://doi.org/10.3389/fmars.2022.982374.
  49. Madan, R., Bhowmick, S., Hadji, L. and Alnujaie, A. (2023), "Limit angular speed analysis of porous functionally graded rotating disk under thermo-mechanical loading", Multidiscip. Model. Ma., 19(2), 311-323.https://doi.org/10.1108/MMMS-09-2022-0197.
  50. Masoodi, A.R. and Arabi, E. (2018), "Geometrically nonlinear thermomechanical analysis of shell-like structures", J. Therm. Stresses, 41(1), 37-53. https://doi.org/10.1080/01495739.2017.1360166
  51. Mirjavadi, S.S., Mohasel Afshari, B., Shafiei, N., Rabby, S. and Kazemi, M. (2018), "Effect of temperature and porosity on the vibration behavior of two-dimensional functionally graded micro-scale Timoshenko beam", J. Vib. Control, 24(18), 4211-4225. https://doi.org/10.1177/1077546317721871.
  52. Monge, J.C., Mantari, J.L. and Arciniega, R.A. (2022), "3D semi-analytical solution of hygro-thermo-mechanical multilayered doubly-curved shells", Eng. Struct., 256, 113916. https://doi.org/10.1016/j.engstruct.2022.113916.
  53. Pan, H., Song, T. and Ge, H. (2021). "A probabilistic study on the mixed-mode fracture in functionally graded materials", Eng. Fail. Anal., 120, 105038. https://doi.org/10.1016/j.engfailanal.2020.105038.
  54. Penna, R., Feo, L., Lovisi, G. and Fabbrocino, F. (2021), "Hygro-thermal vibrations of porous FG nano-beams based on local/nonlocal stress gradient theory of elasticity", Nanomaterials-basel, 11(4), 910. https://doi.org/10.3390/nano11040910.
  55. Qiao, Y. and Yao, G. (2022), "Stability and nonlinear vibration of an axially moving plate interacting with magnetic field and subsonic airflow in a narrow gap", Nonlinear Dynam., 1-22. https://doi.org/10.1007/s11071-022-07805-9.
  56. Raj, S.K., Sahoo, B., Nayak, A.R. and Panda, L.N. (2022), "Parametrically excited axially accelerating viscoelastic beam subjected to time-varying axial speed, longitudinally varying axial tension and internal resonance", Int. J. Nonlinear Mech., 147, 104213. https://doi.org/10.1016/j.ijnonlinmec.2022.104213.
  57. Rezaiee-Pajand, M. and Masoodi, A.R. (2022), "Hygro-thermo-elastic nonlinear analysis of functionally graded porous composite thin and moderately thick shallow panels", Mech. Adv. Mater. Struc., 29(4), 594-612. https://doi.org/10.1080/15376494.2020.1780524.
  58. Rezaiee-Pajand, M., Masoodi, A.R. and Rajabzadeh-Safaei, N. (2019), "Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures", Steel Compos. Struct., 30(6), 493-516. https://doi.org/10.12989/scs.2019.30.6.493
  59. Rezaiee-Pajand, M. and Masoodi, A.R. (2019). "Analyzing FG shells with large deformations and finite rotations", World J. Eng., 16(5), 636-647. https://doi.org/10.1108/WJE-10-2018-0357.
  60. Shakouri, P., Ghazavi, M.R., Shahgholi, M. and Mohamadi, A. (2022), "Linear dynamic analysis of axially moving cylindrical nanoshells considering surface energy effect with constant velocity", Acta Mech., 233(10), 4231-4246. https://doi.org/10.1007/s00707-022-03310-7.
  61. Shan, W.B. and She, G.L. (2023), "Nonlinear resonance of porous functionally graded nanoshells with geometrical imperfection", Struct. Eng. Mech., 88(4), 355-368. https://doi.org/10.12989/sem.2023.88.4.355.
  62. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stresses, 44(10)1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  63. 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 Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  64. 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.
  65. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  66. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  67. Sobhy, M. and Al Mukahal, F.H.H. (2022), "Wave dispersion analysis of functionally graded GPLs-reinforced sandwich piezoelectromagnetic plates with a honeycomb core", Mathematics-Basel., 10(17), 3207. https://doi.org/10.3390/math10173207.
  68. Soedel, W. (2004), "Vibrations of shells and plates", CRC Press. https://doi.org/10.1121/1.1873932.
  69. Tang, Y. and Ding, Q. (2019). "Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads", Compos. Struct., 225, 111076. https://doi.org/10.1016/j.compstruct.2019.111076.
  70. Wang, J.P., Ge, R.Y. and Tang, Y. (2023), "Application of Interpolating matrix method to study dynamics of axially moving beams made of functionally graded materials", Appl. Sci-basel, 13(3), 1449. https://doi.org/10.3390/app13031449.
  71. Wang, Y.Q. (2018), "Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state", Acta Astronaut., 143, 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004.
  72. Wu, F. and She, G.L. (2023), "Wave propagation in double nano-beams 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. Wu, Z., Zhang, Y. and Yao, G. (2022), "Natural frequency and stability analysis of axially moving functionally graded carbon nanotube-reinforced composite thin plates", Acta Mechanica, 1-23. https://doi.org/10.1007/s00707-022-03439-5.
  74. Xie, Z., Jiao, J. and Wrona, S. (2023a), "The fluid-structure interaction lubrication performances of a novel bearing: experimental and numerical study", Tribology Int., 2023, 179, 108151. https://doi.org/10.1016/j.triboint.2022.108151.
  75. Xie, Z., Yang, K., He, T. and Jiao, J. (2023b), "Experimental and theoretical analysis on the nonlinear rotor-dynamic performances and vibration characteristics of a novel bearing-rotor system", Mech. Syst. Signal Pr., 199, 110416. https://doi.org/10.1016/j.ymssp.2023.110416.
  76. 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.
  77. 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.
  78. 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.
  79. Xu, J.Q. and She, G.L. (2023c), "Resonance behavior of functionally graded carbon nanotube-reinforced composites shells with spinning motion and axial motion", Steel Compos. Struct., 49(3), 325-335. https://doi.org/10.12989/scs.2023.49.3.325.
  80. Xu, J.Q. and She, G.L. (2024), "Thermal post-buckling and primary resonance of porous functionally graded beams: Effect of elastic foundations and geometric imperfection", Comput. Concrete, 32(6), 543-551. https://doi.org/10.12989/cac.2023.32.6.543
  81. 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.
  82. Zenkour, A.M. (2020), "Quasi-3D refined theory for functionally graded porous plates: Displacements and stresses", Phys. Mesomech., 23, 39-53. https://doi.org/10.1134/S1029959920010051.
  83. Zghal, S., Ataoui, D. and Dammak, F. (2022). "Static bending analysis of beams made of functionally graded porous materials", Mech. Based Des. Struc., 50(3), 1012-1029. https://doi.org/10.1080/15397734.2020.1748053.
  84. Zhang, D., Tang, Y., Liang, R., Song, Y. and Chen, L. (2022), "Internal resonance of an axially transporting beam with a two-frequency parametric excitation", Appl. Math. Mech-engl., 1-16. https://doi.org/10.1007/s10483-022-2930-9.
  85. Zhang, F., Cao, Z., Qiao, Y., Liu, D. and Yao, G. (2023), "Parametric vibration stability analysis of an axially moving plate with periodical distributed materials", J. Vib. Eng. Technol., 1-11. https://doi.org/10.1007/s42417-022-00792-6.
  86. Zhang, X.M., Liu, G.R. and Lam, K.Y. (2001), "Vibration analysis of thin cylindrical shells using wave propagation approach", J. Sound Vib., 239(3), 397-403. https://doi.org/10.1006/jsvi.2000.3139.
  87. 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.
  88. 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", Nonlinear Dynam., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  89. 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., https://doi.org/10.1080/15376494.2023.2180556.
  90. 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. Stresses, 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  91. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133
  92. 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.
  93. 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.
  94. Zhang, Y.W., Ding, H.X., She, G.L. and Tounsi, A. (2023d), "Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories", Geomech. Eng., 33(4), 381-391. https://doi.org/10.12989/gae.2023.33.4.381.
  95. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023e), "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.
  96. Zhang, Y.W. and She, G.L. (2024), "Combined resonance of graphene platelets reinforced metal foams cylindrical shells with spinning motion under nonlinear forced vibration", Eng. Struct., 300, 117177. https://doi.org/10.1016/j.engstruct.2023.117177.
  97. 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.
  98. 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.
  99. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L. and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://doi.org/10.12989/anr.2022.13.5.465.
  100. Zhao, Y.B. and Zheng, P.P. (2021), "Parameter analyses of suspended cables subjected to simultaneous combination, super and sub-harmonic excitations", Steel Compos. Struct., 40(2), 203-216. https://doi.org/10.12989/scs.2021.40.2.203.
  101. Zhao, Y.B., Peng, J., Zhao, Y.Y. and Chen, L.C. (2017), "Effects of temperature variations on nonlinear planar free and forced oscillations at primary resonance of suspended cables", Nonlinear Dynam., 89, 2815-2827. https://doi.org/10.1007/s11071-017-3627-6