Geomechanics and Engineering

  • 제35권6호
  • /
  • Pages.637-646
  • /
  • 2023
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Propagation behaviors of guided waves in graphene platelet reinforced metal foam plates

  • Wubin Shan (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Hao Zhong (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Nannan Zhang (Hunan Electrical College of Technology, School of elevator engineering) ;
  • Guilin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • 투고 : 2023.07.21
  • 심사 : 2023.11.27
  • 발행 : 2023.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

At present, the research on wave propagation in graphene platelet reinforced composite plates focuses on the propagation behavior of bulk waves, in which the effect of boundary condition is ignored, there is no literature report on propagation behaviors of guided waves in graphene platelet reinforced metal foams (GPLRMF) plates. In fact, wave propagation is affected by boundary conditions, so it is necessary to study the propagation characteristics of guided waves. The aim of this paper is to solve this problem. The effective performance of the material was calculated using the mixing law. Equations of motion of GPLRMF plate is derived by using Hamilton's principle. Then, the eigenvalue method is used to obtain the expressions of bending wave, shear wave and longitudinal wave, and the degradation verification is carried out. Finally, the effects of graphene platelets (GPLs) volume fraction, elastic foundation, porosity coefficient, GPLs distribution types and porosity distribution types on the dispersion relations are studied. We find that these factors play an important role in the propagation characteristics and phase velocity of guided waves.

키워드

과제정보

The present work is supported by "Natural Science Foundation of Hunan Province" (2022JJ60022).

참고문헌

  1. Abuteir, B.W. and Boutagouga, D. (2022), "Free-vibration response of functionally graded porous shell structures in thermal environments with temperature-dependent material properties", Acta. Mech., 233(11), 4877-4901. https://doi.org/10.1007/s00707-022-03351-y.
  2. Ahmadi, H. and Foroutan, K. (2021), "Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition," Steel. Compos. Struct., 40(4), 555-570. https://doi.org/10.12989/scs.2021.40.4.555.
  3. 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.
  4. 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.
  5. 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.
  6. Allahkarami, F. and Tohidi, H. (2022), "Axisymmetric Postbuckling of Functionally Graded Graphene Platelets Reinforced Composite Annular Plate on Nonlinear Elastic Medium in Thermal Environment", Int. J. Struct. Stab. Dy., 2350034. https://doi.org/10.1142/S0219455423500347.
  7. Alnujaie, A., Akba, E. D., Eltaher, M., and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. http://doi.org/10.12989/gae.2021.24.1.091
  8. Aris, H. and Ahmadi, H. (2022), "Combination resonance analysis of imperfect functionally graded conical shell resting on nonlinear viscoelastic foundation in thermal environment under multi-excitation", J. Vib. Control., 28(15-16), 2121-2144. https://doi.org/10.1177/10775463211006527.
  9. Assie, A.E., Mohamed, S.A., Shanab, R.A., Abo-bakr, R.M. and Eltaher, M.A. (2023), "Static buckling of 2D FG porous plates resting on elastic foundation based on unified shear theories", J. Appl. Comput. Mech., 9(1), 239-258. https://doi.org/10.22055/jacm.2022.41265.3723.
  10. Babaei, M., Kiarasi, F., Hossaeini Marashi, S.M., Ebadati, M., Masoumi, F. and Asemi, K. (2021), "Stress wave propagation and natural frequency analysis of functionally graded graphene platelet-reinforced porous joined conical-cylindrical-conical shell", Wave Random Complex, https://doi.org/10.1080/17455030.2021.2003478.
  11. Basha, M., Daikh, A.A., Melaibari, A., Wagih, A., Othman, R., Almitani, K.H., Hamed, M.A., Abdelrahman, A. and Eltaher, M.A. (2022), "Nonlocal strain gradient theory for buckling and bending of FG-GRNC laminated sandwich plates", Steel. Compos. Struct., 43(5), 639-660. https://doi.org/10.12989/scs.2022.43.5.639.
  12. 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.
  13. 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.
  14. Daikh, A.A., Belarbi, M.O., Salami, S.J., Ladmek, M., Belkacem, A., Houari, M.S.A., Ahmed, H.M. and Eltaher, M.A. (2023), "A three-unknown refined shear beam model for the bending of randomly oriented FG-CNT/fiber-reinforced composite laminated beams rested on a new variable elastic foundation", Acta Mechanica, 1-16. https://doi.org/10.1007/s00707-023-03657-5
  15. Daikh, A.A., Houari, M.S.A., Karami, B., Eltaher, M.A., Dimitri, R. and Tornabene, F. (2021), "Buckling analysis of CNTRC curved sandwich nanobeams in thermal environment", Appl. Sci., 11(7), 3250. https://doi.org/10.3390/app11073250.
  16. 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.
  17. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Archiv. Civil Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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. Tech., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435
  23. 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", Waves Random Complex Media, https://doi.org/10.1080/17455030.2023.2235611.
  24. 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.
  25. 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.
  26. Ebrahimi, F. and Dabbagh, A. (2020), "Viscoelastic wave propagation analysis of axially motivated double-layered graphene sheets via nonlocal strain gradient theory", Wave Random Complex, 30(1), 157-176. https://doi.org/10.1080/17455030.2018.1490505.
  27. Ebrahimi, F. and Seyfi, A. (2022), "On wave propagation characteristics of hygrothermally excited graphene foam plates", Wave Random Complex, https://doi.org/10.1080/17455030.2022.2105416.
  28. Ebrahimi, F., Mohammadi, K. and Barouti, M.M. (2021), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Wave Random Complex, 31(6), 1655-1681. https://doi.org/10.1080/17455030.2019.1694729.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. Hendi, A., Eltaher, M.A, Mohamed, S.A, and Attia, M. (2022), "Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel Compos. Struct., 41(6), 787-802. http://doi.org/10.12989/scs.2021.41.6.787.
  34. Li, C. and Han, Q. (2021), "Analyzing wave propagation in graphene-reinforced nanocomposite annular plates by the semi-analytical formulation", Mech. Adv. Mater. Struc., 28(23), 2385-2398. https://doi.org/10.1080/15376494.2020.1736698.
  35. Li, C. and Han, Q. (2021), "Guided waves propagation in sandwich cylindrical structures with functionally graded graphene-epoxy core and piezoelectric surface layers", J. Sandw. Struct. Mater., 23(8), 3878-3901. https://doi.org/10.1177/1099636220959034.
  36. Li, C., Han, Q., Wang, Z. and Wu, X. (2020), "Analysis of wave propagation in functionally graded piezoelectric composite plates reinforced with graphene platelets", Appl. Math. Model., 81, 487-505. https://doi.org/10.1016/j.apm.2020.01.016.
  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. Mahani, R.B., Eyvazian, A., Musharavati, F., Sebaey, T.A. and Talebizadehsardari, P. (2020), "Thermal buckling of laminated Nano-Composite conical shell reinforced with graphene platelets", Thin. Wall. Struct., 155, 106913. https://doi.org/10.1016/j.tws.2020.106913.
  39. Malikan, M., Wiczenbach, T. and Eremeyev, V.A. (2022), "Thermal buckling of functionally graded piezomagnetic micro-and nanobeams presenting the flexomagnetic effect", Continuum Mech. Thermodynam., 34(4), 1051-1066. https://doi.org/10.1007/s00161-021-01038-8.
  40. Martins, A.D., Goncalves, R. and Camotim, D. (2021), "Post-buckling behaviour of thin-walled regular polygonal tubes subjected to bending", Thin. Wall. Struct., 166, 108106. https://doi.org/10.1016/j.tws.2021.108106.
  41. Melaibari, A., Mohamed, S.A., Assie, A.E., Shanab, R.A. and Eltaher, M.A. (2023), "Static response of 2D FG porous plates resting on elastic foundation using midplane and neutral surfaces with Movable constraints", Mathematics, 10(24), 4784. https:/doi.org/10.3390/math10244784.
  42. Mohamed, S.A., Assie, A.E. and Eltaher, M.A. (2023), "Novel incremental procedure in solving nonlinear static response of 2D-FG porous plates", Thin Wall. Struct., 189, 110779. https://doi.org/10.1016/j.tws.2023.110779.
  43. Nguyen, T.P., Vu, M.D., Cao, V.D. and Vu, H.N. (2021), "Nonlinear torsional buckling of functionally graded graphene-reinforced composite (FG-GRC) laminated cylindrical shells stiffened by FG-GRC laminated stiffeners in thermal environment", Polym. Compos., 42(6), 3051-3063. https://doi.org/10.1002/pc.26038.
  44. Phuong, N.T., Dong, D.T., Van Doan, C. and Nam, V.H. (2022), "Nonlinear buckling of higher-order shear deformable stiffened FG-GRC laminated plates with nonlinear elastic foundation subjected to combined loads", Aerosp. Sci. Technol., 127, 107736. https://doi.org/10.1016/j.ast.2022.107736.
  45. Phuong, N.T., Nam, V.H., Trung, N.T., Duc, V.M., Loi, N.V., Thinh, N.D. and Tu, P.T. (2021), "Thermomechanical postbuckling of functionally graded graphene-reinforced composite laminated toroidal shell segments surrounded by Pasternak's elastic foundation", J. Thermoplast. Compos., 34(10), 1380-1407. https://doi.org/10.1177/0892705719870593.
  46. Ramezani, M., Rezaiee-Pajand, M. and Tornabene, F. (2022), "Nonlinear thermomechanical analysis of GPLRC cylindrical shells using HSDT enriched by quasi-3D ANS cover functions", Thin. Wall. Struct., 179, 109582. https://doi.org/10.1016/j.tws.2022.109582.
  47. Saiah, B., Bachene, M., Guemana, M., Chiker, Y. and Attaf, B. (2022), "On the free vibration behavior of nanocomposite laminated plates contained piece-wise functionally graded graphene-reinforced composite plies", Eng. Struct., 253, 113784. https://doi.org/10.1016/j.engstruct.2021.113784
  48. 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. Dy., 22(6), 2250075. https://doi.org/10.1142/S0219455422500754.
  49. Shahgholian-Ghahfarokhi, D., Rahimi, G., Khodadadi, A., Salehipour, H. and Afrand, M. (2021), "Buckling analyses of FG porous nanocomposite cylindrical shells with graphene platelet reinforcement subjected to uniform external lateral pressure", Mech. Based. Des. Struc., 49(7), 1059-1079. https://doi.org/10.1080/15397734.2019.1704777.
  50. 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.
  51. 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.
  52. 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.
  53. 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.
  54. 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.
  55. 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.
  56. Sun, D. and Luo, S.N. (2012), "Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments", Appl. Math. Model., 36(1), 444-462. https://doi.org/10.1016/j.apm.2011.07.023.
  57. Trang, L.T.N. and Tung, H.V. (2022), "Thermally induced post-buckling of thin CNT-reinforced composite plates under nonuniform in-plane temperature distributions", J. Thermoplast. Compos., 35(12), 2331-2353. https://doi.org/10.1177/0892705720962172.
  58. Van Doan, C., Hung, V.T., Phuong, N.T. and Nam, V.H. (2022), "Torsional buckling and postbuckling behavior of stiffened FG-GRCL toroidal shell segments surrounded by elastic foundation", Int. J. Comput. Mat. Sci., 2350001. https://doi.org/10.1142/S204768412350001X.
  59. 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.
  60. 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.
  61. Xiang, J., Lai, Y.L., Moradi, Z. and Khorami, M. (2023), "Wave propagation phenomenon of functionally graded graphene oxide powder-strengthened nanocomposite curved beam", Solid State Commun., 369, 115193. https://doi.org/10.1016/j.ssc.2023.115193.
  62. 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.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. 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.
  68. Zenkour, A.M. and Sobhy, M. (2022), "Axial magnetic field effect on wave propagation in bi-layer FG graphene platelet-reinforced nanobeams", Eng. Comput., 38(2), 1313-1329. https://doi.org/10.1007/s00366-020-01224-3.
  69. 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.
  70. 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 Dynamics, 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  71. 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.
  72. 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.
  73. 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.
  74. 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.
  75. 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.
  76. 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.
  77. 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.
  78. 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.
  79. 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.
  80. 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.
  81. 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.