Computers and Concrete

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Buckling and forced oscillation of organic nanoplates taking the structural drag coefficient into account

  • Dao Minh Tien (Air Force-Air Defence Technical Institute) ;
  • Do Van Thom (Faculty of Mechanical Engineering, Le Quy Don Technical University) ;
  • Nguyen Thi Hai Van (Faculty of Industrial Education, The University of Danang-University of Technology and Education) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Phung Van Minh (Faculty of Mechanical Engineering, Le Quy Don Technical University) ;
  • Dao Nhu Mai (Institute of Mechanics, Vietnam Academy of Science and Technology)
  • Received : 2023.05.27
  • Accepted : 2023.07.20
  • Published : 2023.12.25
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Abstract

This work is the first to apply nonlocal theory and a variety of deformation plate theories to study the issue of forced vibration and buckling in organic nanoplates, where the effect of the drag parameter inside the structure has been taken into consideration. Whereas previous research on nanostructures has treated the nonlocal parameter as a fixed value, this study accounts for its effect, and finds that its value fluctuates with the thickness of each layer. This is also a new point that no works have mentioned for organic plates. On the foundation of the notion of potential movement, the equilibrium equation is derived, the buckling issue is handled using Navier's solution, and the forced oscillation problem is solved using the finite element approach. Additionally, a set of numerical examples exhibiting the forced vibration and buckling response of organic nanoplates are shown. These findings indicate that the nonlocal parameter and the drag parameter of the structure have a substantial effect on the mechanical responses of organic nanoplates.

Keywords

Acknowledgement

This research is funded by The University of Danang - University of Technology and Education under project number T2022-06-12.

References

  1. Abdelrahman, A., Rabab, A.S., Esen, I. and Mohamed, A.E. (2022a), "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. Abdelrahman, A., Rabab, A.S., Esen, I. and Mohamed, A.E. (2022b), "Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load", Steel Compos. Struct., 42(6), 805-826. https://doi.org/10.12989/scs.2022.42.6.805.
  3. Abdelrahman, A.A., Esen, I., Daikh A.A. and Eltaher, M.A. (2021a), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct. Mach., 2021, 1-24. https://doi.org/10.1080/15397734.2021.1999263.
  4. Abdelrhmaan, A.A., Eltaher, M.A. and Esen, I. (2021b), "Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load", Eur. Phys. J. Plus, 136, 1-21. https://doi.org/10.1140/epjp/s13360-021-01682-8.
  5. Alaa, A.A., Esen, I, Cevat, O., Ramy, S., Mohamed, A.E. and Amr, E.A. (2021), "Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory", Smart Struct. Syst., 28(4), 515-533. https://doi.org/10.12989/sss.2021.28.4.515.
  6. Ardayfio, C. (2019), "Computational design of organic solar cell active layer through genetic algorithm", arXiv preprint arXiv:1910.12401.
  7. Bui, T.Q., Thom, V.D., Lan, H.T.T., Duc, H.D., Satoyuki, T., Dat, T.P., Thien-An, N.V., Tiantang, Y. and Sohichi, H. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B: Eng., 92, 218-241. http://doi.org/10.1016/j.compositesb.2016.02.048.
  8. Cardinaletti, I., Tim, V., Steven, N., Rob, C., Dieter, S., Jaroslav, H., Jelle, V., Dries, D., Jurgen, K., Jan, D.H., Alexis, F., Valentina, S., Thierry, C., Wouter, M., Wim, D. and Jean, V.M. (2018), "Organic and perovskite solar cells for space applications", Sol. Energy Mater. Sol. Cells, 182, 121-127. https://doi.org/10.1016/j.solmat.2018.03.024.
  9. Chang, Y.M. (2021), Solution-Processed Organic Solar Modules with 10% Power Conversion Efficiency, Advanced Science News. https://www.advancedsciencenews.com/solution-processed-organic-solar-modules-with-10-power-conversion-efficiency/
  10. Ding, H.X. and She, G.L. (2023) "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Archiv. Civil Mech. Eng., 23, 97. http://doi.org/10.1007/s43452-023-00634-6.
  11. Dung, N.V., Tho, N.C., Ha, N.M. and Hieu, V.T. (2021), "On the finite element model of rotating functionally graded graphene beams resting on elastic foundation", Math. Prob. Eng., 2021, 1586388. https://doi.org/10.1155/2021/1586388.
  12. Duc, N.D., Seung-Eock, K., Quan, T.Q., Long, D.D. and Anh, V.M. (2018), "Nonlinear dynamic response and vibration of nanocomposite multilayer organic solar cell", Compos. Struct., 184, 1137-1144. https://doi.org/10.1016/j.compstruct.2017.10.064.
  13. Duc, D.H., Thom, D.V, Cong, P.H., Minh, P.V. and Nguyen, N.X. (2022), "Vibration and static buckling behavior of variable thickness flexoelectric nanoplates", Mech. Based Des. Struct. Mach., 2022, 1-29. https://doi.org/10.1080/15397734.2022.2088558.
  14. Duc, H.D., Thom, V.D., Nguyen, X.N., Pham, V.V. and Nguyen, T.T. (2021), "Multi-phase-field modelling of the elastic and buckling behaviour of laminates with ply cracks", Appl. Math. Mod., 94, 68-86. https://doi.org/10.1016/j.apm.2020.12.038.
  15. Doan, H.D., Ashraf, M.Z. and Do, V.T. (2022), "Finite element modeling of free vibration of cracked nanoplates with flexoelectric effects", Euro. Phys. J. Plus., 137, 447. https://doi.org/10.1140/epjp/s13360-022-02631-9.
  16. Do, T.V., Bui, T.Q., Yu, T.T., Pham, D.T. and Nguyen, C.T. (2017), "Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment", J. Comput. Sci., 21, 164-181. https://doi.org/10.1016/j.jocs.2017.06.015.
  17. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  18. Eroglu, M., Koc, M.A., Esen, I. and Kozan, R. (2022), "Train-structure interaction for high-speed trains using a full 3D train model", J. Braz. Soc. Mech. Sci. Eng., 44, 48. https://doi.org/10.1007/s40430-021-03338-1.
  19. Eroglu, M., Koc, M.A. and Esen, I. (2023), "Application of magnetic field to reduce the forced response of steel bridges to high speed train", Int. J. Mech. Sci., 2023, 242. https://doi.org/10.1016/j.ijmecsci.2022.108023.
  20. Esen, I. (2011), "Dynamic response of a beam due to an accelerating moving mass using moving finite element approximation", Math. Compos. Appl., 16(1), 171-182. https://doi.org/10.3390/mca16010171.
  21. Esen, I. (2013), "A new finite element for transverse vibration of rectangular thin plates under a moving mass", Fin. Elem. Anal. Des., 66, 26-35. https://doi.org/10.1016/j.finel.2012.11.005.
  22. Esen, I. (2017), "A modified FEM for transverse and lateral vibration analysis of thin beams under a mass moving with a variable acceleration", Latin Am. J. Sol. Struct., 14, 485-511. https://doi.org/10.1590/1679-78253180.
  23. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", Int. J. Mech. Mater. Des., 17, 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  24. Esen, I., Ozarpa, C. and Eltaher, M.A. (2021a), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261, 113552. https://doi.org/10.1016/j.compstruct.2021.113552.
  25. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2021b), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Compos., 38, 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  26. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2022), "Dynamics analysis of timoshenko perforated microbeams under moving loads", Eng. Compos., 38, 2413-2429. https://doi.org/10.1007/s00366-020-01212-7.
  27. Esen, I. and Ozmen, R. (2022), "Free and forced thermomechanical vibration and buckling responses of functionally graded magneto-electro-elastic porous nanoplates", Mech. Based Des. Struct. Mach., 2022, 1-38. https://doi.org/10.1080/15397734.2022.2152045.
  28. Esmaeili, J. and Mahdi, G. (2022), "Multi-scale finite element investigations into the flexural behavior of lightweight concrete beams partially reinforced with steel fiber", Comput. Concrete, 29(6), 393-405. https://doi.org/10.12989/cac.2022.29.6.393.
  29. Esen, I. and Ozmen, R. (2022), "Thermal vibration and buckling of magneto-electro-elastic functionally graded porous nanoplates using nonlocal strain gradient elasticity", Compos. Struct., 296, 115878. https://doi.org/10.1016/j.compstruct.2022.115878.
  30. Faisal, A.T., Mohamed, A.K., Muzamal, H., Gar, A.N.I.M. and Emad, G. (2021), "Computer visualization approach for rotating FG shell: Assessment with ring supports", Comput. Concrete, 28(6), 559-557. https://doi.org/10.12989/cac.2021.28.6.559.
  31. Gui-Lin, S. (2021a), "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.
  32. Gui-Lin, S., Hai-Bo, L. and Behrouz, K. (2021b), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  33. Gui-Lin, S. and Hao-Xuan, D. (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
  34. Hai, T., Al-Masoudy, M.M., Alsulamy, S., Ouni, M.H.E. Ayvazyan, A. and Kumar, A. (2023), "Moving load analysis on cross/angle-ply laminated composite nanoplates resting on viscoelastic foundation", Compos. Struct., 305, 116540. https://doi.org/10.1016/j.compstruct.2022.116540.
  35. Hamed, M.K. and Masoud, T. (2022), "A size-dependent study on buckling and post-buckling behavior of imperfect piezo-flexomagnetic nano-plate strips", Adv. Nano Res., 12(4), 427-440. https://doi.org/10.12989/anr.2022.12.4.427.
  36. Hao-Xuan, D., Yi-Wen, Z. and Gui-Lin, S. (2022), "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.
  37. Hao-Xuan, D. and Gui-Lin, S. (2023), "Nonlinear primary resonance behavior of graphene platelet-reinforced metal foams conical shells under axial motion", Nonlinear Dyn., 2023, 1-30. https://doi.org/10.1007/s11071-023-08564-x.
  38. Hao-Xuan, D., Eltaher, M.A. and She, G.L. (2023), "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.
  39. Hoang-Nam, N., Canh, T.N., Thanh, T.T., Ke, T.V., Phan, V.D. and Do, V.T. (2019), "Finite element modelling of a composite shell with shear connectors", Symmetry, 11(4), 527. https://doi.org/10.3390/sym11040527.
  40. Hoppe, H. and Sariciftci, N.S. (2004), "Organic solar cells: An overview", J. Mater. Res., 19(7), 1924-1945. https://doi.org/10.1557/JMR.2004.0252.
  41. Koc, M.A., Esen, I. and Eroglu, M. (2023), "Thermomechanical vibration response of nanoplates with magneto-electro-elastic face layers and functionally graded porous core using nonlocal strain gradient elasticity", Mech. Adv. Mat. Struct., 2023, 1-23. https://doi.org/10.1080/15376494.2023.2199412.
  42. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solid., 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  43. Li, Q., Wu, D., Gao, W., Tin-Loi, F., Liu, Z. and Cheng, J. (2019), "Static bending and free vibration of organic solar cell resting on Winkler-Pasternak elastic foundation through the modified strain gradient theory", Eur. J. Mech. A/Solids, 78, 103852. https://doi.org/10.1016/j.euromechsol.2019.103852.
  44. Li, Q., Wu, D., Gao, W. and Tin-Loi, F. (2020), "Size-dependent instability of organic solar cell resting on Winkler-Pasternak elastic foundation based on the modified strain gradient theory", Int. J. Mech. Sci., 177, 105306. https://doi.org/10.1016/j.ijmecsci.2019.105306.
  45. Liu, S., Wang, K., Wang, B., Li, J. and Zhang, C. (2022), "Size effect on thermo-mechanical instability of micro/nano scale organic solar cells", Meccanica, 57(1), 87-107. https://doi.org/10.1007/s11012-021-01411-6.
  46. Liang, Z. and Tzu-Hsing, K. (2022), "Bending and buckling of spinning FG nanotubes based on NSGT", Comput. Concrete, 30(4), 243-256. https://doi.org/10.12989/cac.2022.30.4.243.
  47. Luat, D.T., Thom, D.V., Thanh, T.T., Minh, P.V., Ke, T.V. and Vinh, P.V. (2021), "Mechanical analysis of bi-functionally graded sandwich nanobeams", Adv. Nano Res., 11(1), 55-71. https://doi.org/10.12989/anr.2021.11.1.055.
  48. Loghman, E., Kamali, A., Bakhtiari-Nejad, F. and Abbaszadeh, M. (2021), "Nonlinear free and forced vibrations of fractional modeled viscoelastic FGM micro-beam", Appl. Math. Mod., 92, 297-314. https://doi.org/10.1016/j.apm.2020.11.011.
  49. Lu, L., Gui-Lin, S. and Xingming, G. (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.
  50. Mashhour, A.A., Esen, I., Alaa A.A., Azza, M.A. and Mohamed, A.E. (2022) "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load", Adv. Nano Res., 12(3), 231-251. https://doi.org/10.12989/anr.2022.12.3.231.
  51. Minh, P.V. and Ke, T.V. (2022), "A comprehensive study on mechanical responses of non-uniform thickness piezoelectric nanoplates taking into account the flexoelectric effect", Arab J. Sci. Eng., 2022, 1-26. https://doi.org/10.1007/s13369-022-07362-8.
  52. Nehm, F., Pfeiffelmann, T., Dollinger, F., Muller-Meskamp, L. and Leo, K. (2017), "Influence of aging climate and cathode adhesion on organic solar cell stability", Sol. Energy Mater. Sol. Cells, 168, 1-7. https://doi.org/10.1016/j.solmat.2017.03.037.
  53. Nam, V.H., Doan, D.H., Khoa, N.M., Do, T.V. and Tran, H.T. (2019a), "Phase-field buckling analysis of cracked stiffened functionally graded plates", Compos. Struct., 217, 50-59. https://doi.org/10.1016/j.compstruct.2019.03.014.
  54. Nam, N.H., Tan, T.C., Luat, D.T., Phan, V.D., Thom, D.V. and Minh, P.V. (2019b), "Research on the buckling behavior of functionally graded plates with stiffeners based on the third-order shear deformation theory", Mater., 12(8), 1262. http://dx.doi.org/10.3390/ma12081262.
  55. Naderi, A. (2022), "The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis", Proc. Inst. Mech. Eng. Part N, 236(1-2), 41-48. https://doi.org/10.1177/2397791421102982.
  56. Nguyen, H.N., Nguyen, T.Y., Tran, V.K., Tran, T.T., Nguyen, T.T., Phan, V.D. and Thom, D.V. (2019), "A finite element model for dynamic analysis of triple-layer composite plates with layers connected by shear connectors subjected to moving load", Mater., 12(4), 598. https://doi.org/10.3390/ma12040598.
  57. Nguyen, C.T., Thom, D.V., Pham, H.C., Ashraf, M.Z., Duc, H.D. and Phung, V.M. (2023), "Finite element modeling of the bending and vibration behavior of three-layer composite plates with a crack in the core layer", Compos. Struct., 305, 116529. https://doi.org/10.1016/j.compstruct.2022.116529.
  58. Jin, Q. and Ren, Y. (2022), "Nonlinear size-dependent bending and forced vibration of internal flow-inducing pre- and post-buckled FG nanotubes", Commun. Nonlinear Sci. Numer. Simul., 104, 106044. https://doi.org/10.1016/j.cnsns.2021.106044.
  59. Thai, L.M., Luat, D.T., Phung, V.B., Minh, P.V. and Thom, D.V. (2022), "Finite element modeling of mechanical behaviors of piezoelectric nanoplates with flexoelectric effects", Arch. Appl. Mech., 92(1), 163-182. http://doi.org/10.1007/s00419-021-02048-3.
  60. Thom, D.V., Duc, D.H., Minh, P.V. and Tung, N.S. (2020), "Finite element modelling for free vibration response of cracked stiffened fgm plates", Vietnam J. Sci. Technol., 58(1), 119-129. http://doi.org/10.15625/2525-2518/58/1/14278.
  61. Thom, V.D., Duc, H.D., Nguyen, C.T. and Nguyen, D.D. (2022), "Thermal buckling analysis of cracked functionally graded plates", Int. J. Struct. Stab. Dyn., 22(8), 2250089. https://doi.org/10.1142/S0219455422500894.
  62. Thom, V.D, Vinh, V.P. and Hoang, N.N. (2020), "On the development of refined plate theory for static bending behavior of functionally graded plates", Math. Prob. Eng., 2020, 2836763. https://doi.org/10.1155/2020/2836763.
  63. Thom, D.V., Doan, D.H., Duc, N.D. and Bui, T.Q. (2017), "Phase-field thermal buckling analysis for cracked functionally graded composite plates considering neutral surface", Compos. Struct., 182, 542-548. http://doi.org/10.1016/j.compstruct.2017.09.059.
  64. Tavakkoli, M., Ajeian, R., Badrabadi, M.N., Ardestani, S.S., Feiz, S.M.H. and Nasab, K.E. (2011), "Progress in stability of organic solar cells exposed to air", Sol. Energy Mater. Sol. Cells, 95(7), 1964-1969. https://doi.org/10.1016/j.solmat.2011.01.029.
  65. Tuyen, B.V. (2022), "Free vibration behaviors of nanoplates resting on viscoelastic medium", Arab. J. Sci. Eng., 2022, 1-14. https://doi.org/10.1007/s13369-022-07500-2.
  66. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  67. Tuan, L.T., Dung, N.T., Thom, D.V., Minh, P.V. and Zenkour, A. (2021), "Propagation of non-stationary kinematic disturbances from a spherical cavity in the pseudo-elastic cosserat medium", Eur. Phys. J. Plus, 136, 1199. https://doi.org/10.1140/epjp/s13360-021-02191-4.
  68. Tien, D.M., Thom, D.V., Minh, P.V., Tho, N.C., Doan, T.N. and Mai, D.N. (2023), "The application of the nonlocal theory and various shear strain theories for bending and free vibration analysis of organic nanoplates", Mech. Based Des. Struct. Mach., 2023, 1-23. https://doi.org/10.1080/15397734.2023.2186893.
  69. Tinh, Q.B., Duc, H.D., Thom, V.D., Sohichi, H. and Nguyen, D.D. (2016), "High frequency modes meshfree analysis of Reissner-Mindlin plates", J. Scie.: Adv. Mater. Dev., 1(3), 400-412. https://doi.org/10.1016/j.jsamd.2016.08.005.
  70. Tran, N.D., Thom, D.V., Thanh, N.T., Chuong, P.V., Tho, N.C., Ta, N.T. and Nguyen, H.N. (2020), "Analysis of stress concentration phenomenon of cylinder laminated shells using higher-order shear deformation Quasi-3D theory", Compos. Struct., 232, 111526. https://doi.org/10.1016/j.compstruct.2019.111526.
  71. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40, 137-146. https://doi.org/10.2514/3.15006.
  72. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3-4), 195-220. https://doi.org/10.1007/BF01176650.
  73. Sobhy, M. (2014), "Natural frequency and buckling of orthotropic nanoplates resting on two-parameter elastic foundations with various boundary conditions", J. Mech., 30, 443-453. https://doi.org/10.1017/jmech.2014.46.
  74. Sobhy, M. and Ahmed, F.R. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(1), 1750008. https://doi.org/10.1142/S1758825117500089.
  75. Song, M., Sritawat, K. and Jie, Y. (2017), "Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Struct., 159, 579-588. http://doi.org/10.1016/j.compstruct.2016.09.070.
  76. O'Connor, T.F., Aliaksandr, V.Z., Suchol, S., Adam, D.P., Cameron, D.W., Mare, I.D., Eric, J.S. and Darren, J.L. (2016), "Wearable organic solar cells with high cyclic bending stability: Materials selection criteria", Sol. Energy Mater. Sol. Cells, 144, 438-444. https://doi.org/10.1016/j.solmat.2015.09.049.
  77. Ozmen, R., Kilic, R. and Esen, I. (2022), "Thermomechanical vibration and buckling response of nonlocal strain gradient porous fg nanobeams subjected to magnetic and thermal fields", Mech. Adv. Mater. Struct., 2022, 1-20. https://doi.org/10.1080/15376494.2022.2124000.
  78. Pham, T.D., Doan, T.L. and Do, V.T. (2016), "Free vibration of functionally graded sandwich plates with stiffeners based on the third-order shear deformation theory", Viet. J. Mech., 38(2), 103-122. https://doi.org/10.15625/0866-7136/38/2/6730.
  79. Pham, T.D., Pham, Q.H., Phan, V.D., Nguyen, H.N. and Do, V.T. (2019), "Free vibration analysis of functionally graded shells using an edge-based smoothed finite element method", Symmetry, 11(5), 684. https://doi.org/10.3390/sym11050684.
  80. Pei, Y.L., Geng, P.S. and Li, L.X. (2018), "A modified higher-order theory for FG beams", Eur. J. Mech. A/Solids, 72, 186-197. https://doi.org/10.1016/j.euromechsol.2018.05.008.
  81. Quang, D.V., Doan T.N., Luat, D.T. and Thom, D.V. (2022), "Static analysis and boundary effect of FG-CNTRC cylindrical shells with various boundary conditions using quasi-3D shear and normal deformations theory", Struct., 44, 828-850. https://doi.org/10.1016/j.istruc.2022.08.039.
  82. Vu, H.N., Nam, N.H., Vinh, P.V., Khoa, D.N., Thom, D.V. and Minh, P.V. (2019), "A new efficient modified first-order shear model for static bending and vibration behaviors of two-layer composite plate", Adv. Civil Eng., 2019, 2174080. https://doi.org/10.1155/2019/2174080.
  83. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  84. Yi-Wen, Z., Gui-Lin, S. and Hao-Xuan, D. (2023), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A/Solids, 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  85. Yi-Wen, Z. and She, G.L. (2023), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Struct., 2023, 1-13. https://doi.org/10.1080/15376494.2023.2180556.
  86. Yu, T., Tinh, Q.B., Shuohui, Y., Duc, H.D., Wu, C.T., Thom, V.D. and Satoyuki, T. (2016), "On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis", Compos. Struct., 136, 684-695. http://dx.doi.org/10.1016/j.compstruct.2015.11.002.
  87. Zhang, Y.W. and She, G.L. (2023), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear Dyn., 111, 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  88. Wan, P.H., Al-Furjan, M.S.H., Kolahchi, R. and Shan, L. (2023), "Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs' waviness and agglomeration", Mech. Syst. Sign. Proc., 189, 110064. https://doi.org/10.1016/j.ymssp.2022.110064.
  89. Wu, Z., Zhang, Y. and Huan, Z. (2019), "Solving post-buckling characteristic of thermal-resistance films attached to glass facade via an optimization method", Int. J. Struct. Stab. Dyn., 19(6), 2019. https://doi.org/10.1142/S0219455419500688.