Advances in nano research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Wave propagation in FG polymer composite nanoplates embedded in variable elastic medium

  • Ahmed Kadiri (Faculty of Technology, Department of Basic Teaching in Science and Technology, University of Sidi Bel Abbes) ;
  • Mohamed Bendaida (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Amina Attia (Engineering and Sustainable Development Laboratory, Faculty of Science and Technology, Civil Engineering Department, University of Ain Temouchent) ;
  • Mohammed Balubaid (Department of Industrial Engineering, King Abdulaziz University) ;
  • S. R. Mahmoud (GRC Department, Applied College, King Abdulaziz University) ;
  • Abdelmoumen Anis Bousahla (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Abdeldjebbar Tounsi (Mechanical Engineering Department, Faculty of Science & Technology, University of Relizane) ;
  • Fouad Bourada (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2024.05.25
  • Accepted : 2024.08.28
  • Published : 2024.09.25
⟨ Previous Next ⟩

Abstract

This study explores the transmission of waves through polymer composite nanoplates situated on varying elastic foundations. The reinforcement of these nanoplates is assured by graphene nanoplatelets (GNP). Furthermore, the material's behavior is assessed using the Halpin-Tsai model, while the precise representations of stress and strain effects are ensured by the four variables higher order shear deformation theory. The equations of motion are obtained and resolved through the application of Hamilton's principle and the trial function. The study examines how different factors, like the nonlocal parameter, strain gradient parameter, weight fraction, and variable elastic foundations affect the outcomes of wave propagation in nanoplates. This thorough investigation offers valuable insights into the difficult behavior of wave dynamics in nanoplates, this has led to substantial advancements in engineering applications for the future.

Keywords

Acknowledgement

This research work was funded by Institutional Fund Projects under grant no. (IFPIP_ 1569-135-1443). Therefore, the authors gratefully acknowledge technical and financial support from the Ministry of Education and King Abdulaziz University, Jeddah, Saudi Arabia.

References

  1. Abdelrahman, A.A., Esen, I., Tharwan, M.Y., Assie, A. and Eltaher, M.A. (2024), "On vibrations of functionally graded carbon nanotube (FGCNT) nanoplates under moving load", Adv. Nano Res., 16(4), 395-412. https://doi.org/10.12989/anr.2024.16.4.395.
  2. Abed Z.A.K. and Majeed, W.I. (2020), "Effect of boundary conditions on harmonic response of laminated plates", Compos. Mater. Eng., 2(2), 125-140. https://doi.org/10.12989/cme.2020.2.2.125.
  3. Aditya, N.D., Ben, Z.T., Polit, O., Pradyumna B. and Ganapathi, M. (2019), "Large amplitude free flexural vibrations of functionally graded graphene platelets reinforced porous composite curved beams using finite element based on trigonometric shear deformation theory", Int. J. Nonlinear. Mech., 116, 302-317. https://doi.org/10.1016/j.ijnonlinmec.2019.07.010.
  4. Ahmed, R.A., Fenjan, R.M., Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  5. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/SCS.2015.19.6.1421.
  6. Akgoz, B. and Civalek, O. (2017), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.03
  7. Akgoz, B. and Civalek, O. (2017b), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng., 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024
  8. Al-Basyouni, K.S., Ghandourah, E., Mostafa, H.M. and Algarni, A. (2020), "Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body", Geomech. Eng., 21(1), 1-9. https://doi.org/10.12989/GAE.2020.21.1.001.
  9. Al-Furjan, M.S.H., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2021), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Semi-numerical and finite element modeling", Thin Wall. Struct., 159, 107242. https://doi.org/10.1016/j.tws.2020.107242
  10. Almitani, K.H., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Stability of perforated nanobeams incorporating surface energy effects", Steel Compos. Struct., 35(4), 555-566. https://doi.org/10.12989/scs.2020.35.4.555.
  11. Ansari, R., Shahabodini, A. and Shojaei, M.F. (2016), "Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations", Physica E, 76, 70-81. https://doi.org/10.1016/j.physe.2015.09.042
  12. Apuzzo, A., Barretta, R., Faghidian, S.A., Luciano, R. and Marotti de Sciarra, R. (2018), "Free vibrations of elastic beams by modified nonlocal strain gradient theory", Int. J. Eng. Sci., 133, 99-108. https://doi.org/10.1016/j.ijengsci.2018.09.002.
  13. Arefi, M., Bidgoli, E.M.R. and Rabczuk, T. (2019), "Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST", Eur. J. Mech. A Solid., 77, 103802. https://doi.org/10.1016/j.euromechsol.2019.103802.
  14. Arefi, M., Bidgoli, M.R., Dimitri, R. and Tornabene, F. (2018), "Free vibrations of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Aerosp. Sci. Technol., 81, 108-117. https://doi.org/10.1016/j.ast.2018.07.036.
  15. Attia, M.A. and Mahmoud, F.F. (2016), "Modeling and analysis of nanobeams based on nonlocal-couple stress elasticity and surface energy theories", Int. J. Mech. Sci., 105, 126-134. https://doi.org/10.1016/j.ijmecsci.2015.11.002
  16. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  17. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/SCS.2019.30.6.603
  18. Barretta, R. and de Sciarra, F.M. (2018), "Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams", Int. J. Eng. Sci., 130, 187-198. https://doi.org/10.1016/j.ijengsci.2018.05.009.
  19. Barretta, R., Sciarra, F.M.d. and Vaccaro, M.S. (2019), "On nonlocal mechanics of curved elastic beams", Int. J. Eng. Sci., 144, 103140. http://doi.org/10.1016/j.ijengsci.2019.1031.
  20. Behdinan, K. and Moradi-Dastjerdi, R. (2022), "Thermal buckling resistance of a lightweight lead-free piezoelectric nanocomposite sandwich plate", Adv. Nano Res., 12(6), 593-603. https://doi.org/10.12989/ANR.2022.12.6.593
  21. Bharath, H.S., Waddar, S., Bekinal, S.I., Jeyaraj, P. and Doddamani, M. (2020), "Effect of axial compression on dynamic response of concurrently printed sandwich", Compos. Struct., 113223. https://doi.org/10.1016/j.compstruct.2020.113223.
  22. Bochkareva, S.A. and Lekomtsev, S.V. (2022), "Natural vibrations and hydroelastic stability of laminated composite circular cylindrical shells", Struct. Eng. Mech., 81(6), 769-780. https://doi.org/10.12989/SEM.2022.81.6.769
  23. Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289, 335-352. https://doi.org/10.1016/j.amc.2016.05.034.
  24. Daouadji, T.H. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/GAE.2015.9.5.631.
  25. Ding, F., Ding, H., He, C., Wang, L. and Lyu, F. (2022), "Method for flexural stiffness of steel-concrete composite beams based on stiffness combination coefficients", Comput. Concr., 29(3), 127-144. https://doi.org/10.12989/CAC.2022.29.3.127
  26. Ding, H.X., Liu, H.B., She, G.L. and Wu, F. (2023), "Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory", Comput. Concr., 32(2), 207-215. https://doi.org/10.12989/CAC.2023.32.2.207
  27. Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates", Eur. Phys. J. Plus, 133, 151. https://doi.org/10.1140/epjp/i2018-11956-5.
  28. Ebrahimi, F., Barati, M.R. and Civalek, O. (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964. https://doi.org/10.1007/s00366- 019-00742-z.
  29. Ebrahimi, F., Seyfi, A., Dabbagh, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Sci., 71, 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  30. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2021), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Waves Random Complex Med., 31(6), 1655-1681. https://doi.org/10.1080/17455030.2019.1694729
  31. Eltaher, M.A., Almalki, T.A., Ahmed, K.I.E. and Almitani, K.H. (2019), "Characterization and behaviors of single walled carbon nanotube by equivalent-continuum mechanics approach", Adv. Nano Res., 7(1), 39-49. https://doi.org/10.12989/ANR.2019.7.1.039
  32. Eltaher, M.A. and Abdelrahman, A.A. (2020), "Bending behavior of squared cutout nanobeams incorporating surface stress effects", Steel Compos. Struct., 36(2), 143-161. https://doi.org/10.12989/scs.2020.36.2.143.
  33. Eltaher, M.A. and Mohamed, N. (2020), "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311
  34. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51-64. https://doi.org/10.12989/ANR.2016.4.1.051
  35. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and Alshorbagy, A.E. (2020), "Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts", Smart. Struct. Syst., 25(2), 219-228. https://doi.org/10.12989/sss.2020.25.2.219
  36. Emam, S.A., Eltaher, M.A., Khater, M.E. and Abdalla, W.S. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci. Basel, 8(11), 2238. https://doi.org/10.3390/app8112238
  37. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2023), "The surface stress effects on the buckling analysis of porous micro-composite annular sandwich plate based on HSDT using Ritz method", Comput. Concr., 32(5), 439-454. https://doi.org/10.12989/CAC.2023.32.5.439
  38. Eringen, A.C. (1998), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  39. Esen, I., Alazwari, M.A., Almitani, K.H., Eltaher, M.A. and Abdelrahman, A. (2023), "Dynamic vibration response of functionally graded porous nanoplates in thermal and magnetic fields under moving load", Adv. Nano Res., 14(5), 475-493. https://doi.org/10.12989/ANR.2023.14.5.475
  40. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  41. Gao, W., Qin, Z. and Chu, F. (2020), "Wave propagation in functionally graded porous plates reinforced with grapheme platelets", Aerosp. Sci. Technol., 102, 105860. https://doi.org/10.1016/j.ast.2020.10586.
  42. Gao, Y., Xiao, W. and Zhu, H. (2019), "Nonlinear vibration analysis of different types of functionally graded beams using nonlocal strain gradient theory and a two-step perturbation method", Euro. Phys. J. Plus, 134(1), 23. https://doi.org/10.1140/epjp/i2019-12446-0
  43. Ghayesh, M.H. and Farajpour, A. (2018), "Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory", Int. J. Eng. Sci., 129, 84-95. https://doi.org/10.1016/j.ijengsci.2018.04.003.
  44. Ghayesh, M.H., Farokhi, H. and Farajpour, A. (2019), "Global dynamics of fluid conveying nanotubes", Int. J. Eng. Sci., 135, 37-57. https://doi.org/10.1016/j.ijengsci.2018.11.003
  45. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.
  46. Hadji, L., Meziane, A. and Safa, A. (2018), "A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 66(6), 771-781. https://doi.org/10.12989/sem.2018.66.6.771
  47. Hou, S., Wu, S., Luo, J., Nasihatgozar, M. and Behshad, A. (2022), "Frequency response of elastic nanocomposite beams containing nanoparticles based on sinusoidal shear deformation beam theory", Steel Compos. Struct., 45(4), 555-562. https://doi.org/10.12989/SCS.2022.45.4.555
  48. Hua, F., Fu, W. and Zhou, X. (2022), "Guided wave propagation in functionally graded viscoelastic polymer composite shells reinforced with graphite particles", Wave Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2022.2091180
  49. Hua, F., Fu, W. and Zhou, X. (2022), "Wave propagation analysis of sandwich plates with graphite particles filled viscoelastic material core in hygrothermal environments", Compos. Struct., 288, 115380. https://doi.org/10.1016/j.compstruct.2022.115380
  50. Hua, F., Fu, W., You, Q. and Zhou, X. (2022), "Wave dispersion characteristics of laminated carbon fiber reinforced polymer composite shells resting on viscoelastic foundations under thermal field", Compos. Struct., 301, 116225. https://doi.org/10.1016/j.compstruct.2022.116225
  51. Hua, F., Fu, W., You, Q., Huang, Q., Abad, F. and Zhou, X. (2023), "A refined spectral element model for wave propagation in multiscale hybrid epoxy/carbon fiber/graphene platelet composite shells", Aerosp. Sci. Technol., 138, 108321. https://doi.org/10.1016/j.ast.2023.108321
  52. Hua, F., Huang, Q., You, Q., He, W., Zhou, H. and Zhou, X. (2024), "A semi-analytical spectral element model for guided wave propagation in composite laminated conical shells", Structures, 65, 106797. https://doi.org/10.1016/j.istruc.2024.106797
  53. Huang, Y. and Wu, S. (2022), "Hybrid adaptive neuro fuzzy inference system for optimization mechanical behaviors of nanocomposite reinforced concrete", Adv. Nano Res., 12(5), 515-527. https://doi.org/10.12989/ANR.2022.12.5.515
  54. Janghorban, M. and Tounsi, A. (2024), "Two models for wave propagation in polymer/halloysite nanotube nanocomposites: network phenomena/generalized continuum mechanics", Wave Random Complex Med., 1-32. https://doi.org/10.1080/17455030.2024.2396335
  55. Jiao, P. and Alavi, A.H. (2018), "Buckling analysis of graphene-reinforced mechanical metamaterial beams with periodic webbing patterns", Int. J. Eng. Sci., 131, 1-18. https://doi.org/10.1016/j.ijengsci.2018.06.005.
  56. Kamarian, S. and Song, J.I. (2023), "Thermal buckling of rectangular sandwich plates with advanced hybrid SMA/CNT/graphite/epoxy composite face sheets", Adv. Nano Res., 14(3), 261-271. https://doi.org/10.12989/ANR.2023.14.3.261
  57. Karami, B., Janghorban, M. and Rabczuk, T. (2019), "Analysis ofelastic bulk waves in functionally graded triclinic nano-platesusing a quasi-3D bi-Helmholtz nonlocal strain gradient model", Euro. J. Mech. A Solid., 78, 103822. https://doi.org/10.1016/j.euromechsol.2019.103822
  58. Khatri, K.L. and Markad, K. (2023), "Stochastic fracture behavior analysis of infinite plates with a separate crack and a hole under tensile loading", Comput. Concr., 32(1), 99-117. https://doi.org/10.12989/CAC.2023.32.1.099
  59. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stress., 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  60. Kim, D.Y., Sim, C.H., Park, J.S., Yoo, J.T., Yoon, Y.H. and Lee, K. (2023), "Numerical vibration correlation technique analyses for composite cylinder under compression and internal pressure", Struct. Eng. Mech., 87(5), 419-429. https://doi.org/10.12989/SEM.2023.87.5.419
  61. 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.2020.01.01.
  62. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.00.
  63. Liu, H., Wu, H. and Lyu, Z. (2020), "Nonlinear resonance of FG multilayer beam-type nanocomposites: Effects of grapheme nanoplatelet-reinforcement and geometric imperfection", Aerosp. Sci. Technol., 98, 105702. https://doi.org/10.1016/j.ast.2020.105702.
  64. Lu, L., Guo, X. and Zhao, J. (2018), "On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy", Int. J. Eng. Sci., 124, 24-40. https://doi.org/10.1016/j.ijengsci.2017.11.020.
  65. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  66. Madenci, E. and O zutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097.
  67. Madenci, E., Gulcu, S. and Draiche, K. (2024), "Analytical nonlocal elasticity solution and ANN approximate for free vibration response of layered carbon nanotube reinforced composite beams", Adv. Nano Res., 16(3), 251-263. https://doi.org/10.12989/ANR.2024.16.3.251
  68. Malikan, M., Krasheninnikov, M. and Eremeyev, V.A. (2020), "Torsional stability capacity of a nano-composite shell based on a nonlocal strain gradient shell model under a three-dimensional magnetic field", Int. J. Eng. Sci., 148, UNSP 103234. https://doi.org/10.1016/j.ijengsci.2019.10321
  69. Malikan, M., Tornabene, F. and Dimitri, R. (2018), "Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals", Mater. Res. Exp., 5(9), 095006. https://doi.org/10.1088/2053-1591/aad4c3
  70. Man, Y. (2022), "On the dynamic stability of a composite beam via modified high-order theory", Comput. Concr., 30(2), 151-164. https://doi.org/10.12989/CAC.2022.30.2.151
  71. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. https://doi.org/10.12989/ANR.2019.7.3.181.
  72. Mehar, K., Panda, S.K., Yuvarajan, D., Gautam, C. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., S0263822318344763. https://doi.org/10.1016/j.compstruct.2019.03.002.
  73. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361.
  74. Mohamed, N., Mohamed, S.A., Abdelrhmaan, A.A. and Eltaher, M.A. (2023), "Nonlinear stability of bio-inspired composite beams with higher order shear theory", Steel Compos. Struct., 46(6), 759-772. https://doi.org/10.12989/SCS.2023.46.6.759
  75. Moradi, S. and Mansouri, M.H. (2012), "Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature", Steel Compos. Struct., 12(2), 129-147. https://doi.org/10.12989/scs.2012.12.2.129.
  76. Panda, S.K., Singh, B.N. (2013), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007.
  77. Pinnola, F.P., Faghidian, S.A., Barretta, R. and Marotti de Sciarra, F. (2020), "Variationally consistent dynamics of nonlocal gradient elastic beams", Int. J. Eng. Sci., 149, 103220. https://doi.org/10.1016/j.ijengsci.2020.103220
  78. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M., Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  79. Sahmani, S.S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs", Compos. Struct., 198, 51-62. https://doi.org/10.1016/j.compstruct.2018.05.031.
  80. Sahoo, S., Parida, S.P. and Jena, P.C. (2023), "Dynamic response of a laminated hybrid composite cantilever beam with multiple cracks & moving mass", Struct. Eng. Mech., 87(6), 529-540. https://doi.org/10.12989/SEM.2023.87.6.529
  81. Sahu, P., Sharma, N. and Panda, S.K. (2020), "Numerical prediction and experimental validation of free vibration responses of hybrid composite (glass/carbon/kevlar) curved panel structure", Compos. Struct., 112073. https://doi.org/10.1016/j.compstruct.2020.112073.
  82. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/SSS.2020.26.3.361.
  83. Shanab, R.A., Mohamed, N.A., Eltaher, M.A. and Abdelrahman, A.A. (2023), "Dynamic characteristics of viscoelastic nanobeams including cutouts", Adv. Nano Res., 14(1), 45-65. https://doi.org/10.12989/ANR.2023.14.1.045
  84. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct, 37(1), 27-35. https://doi.org/10.12989/scs.2020.37.1.027
  85. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct., 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179.
  86. Singh, V.K. and Panda, S.K. (2014), "Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels", Thin Wall. Struct., 85, 341-349. https://doi.org/10.1016/j.tws.2014.09.003.
  87. Sobhy, M. (2015), "A comprehensive study on FGM nanoplates embedded in an elastic medium", Compos. Struct., 134, 966-980. https://doi.org/10.1016/j.compstruct.2015.08.102
  88. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B Eng., 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043
  89. Taherifar, R., Mahmoudi, M., Nasr Esfahani, M.H., Khuzani, N.A., Esfahani, S.N. and Chinaei, F. (2019), "Buckling analysis of concrete plates reinforced by piezoelectric nanoparticles", Comput. Concr., 23(4), 295-301. https://doi.org/10.12989/cac.2019.23.4.295
  90. Tayebi, M.S., Salami, S.J. and Tavakolian, M. (2023), "Free vibration analysis of FG composite plates reinforced with GPLs in thermal environment using full layerwise FEM", Struct. Eng. Mech., 85(4), 445-459. https://doi.org/10.12989/SEM.2023.85.4.445
  91. Thai, H.T., Park, T. and Choi, D.H. (2013), "An efficient shear deformation theory for vibration of functionally graded plates", Arch. Appl. Mech., 83, 137-149. https://doi.org/10.1007/s00419-012-0642-4
  92. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concr., 26(1), 53-62. https://doi.org/10.12989/CAC.2020.26.1.053.
  93. Tounsi, A., Tahir, S.I., Mudhaffar, I.M., Al-Osta, M.A. and Chikh, A. (2024), "On the wave propagation characteristics of functionally graded porous shells", HCMCOU J. Sci. Adv. Comput. Struct., 14(1).
  94. Tran, T.T., Tran, V.K., Le, P.B., Phung, V.M., Do, V.T. and Nguyen, H.N. (2020). "Forced vibration analysis of laminated composite shells reinforced with graphene nanoplatelets using finite element method", Adv. Civil Eng., 1471037. https://doi.org/10.1155/2020/1471037
  95. Turan, F. (2023), "Stability of the porous orthotropic laminated composite plates via the hyperbolic shear deformation theory", Steel Compos. Struct., 48(2), 145-161. https://doi.org/10.12989/SCS.2023.48.2.145
  96. Turini, T.T. and Calenzani, A.F.G. (2022), "Analytical study of composite steel-concrete beams with external prestressing", Struct. Eng. Mech., 82(5), 595-609. https://doi.org/10.12989/SEM.2022.82.5.595
  97. Uzun, B. and Civalek, O. (2019), "Nonlocal FEM formulation for vibration analysis of nanowires on elastic matrix with different materials", Math. Comput. Appl., 24(2), 38. https://doi.org/doi:10.3390/mca2402003
  98. Vantadori, S., Luciano, R., Scorza, D. and Darban, H. (2022), "Fracture analysis of nanobeams based on the stress-driven nonlocal theory of elasticity", Mech. Adv. Mater. Struct., 29(14), 1967-1976. https://doi.org/10.1080/15376494.2020.1846231
  99. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  100. Wang, X., Guo, X., Babaei, M., Fili, R. and Farahani, H. (2023), "Natural frequency analysis of joined conical-cylindrical-conical shells made of graphene platelet reinforced composite resting on Winkler elastic foundation", Adv. Nano Res., 15(4), 367-384. https://doi.org/10.12989/ANR.2023.15.4.367
  101. Wu, X. (2023), "Nonlinear finite element vibration analysis of functionally graded nanocomposite spherical shells reinforced with graphene platelets", Adv. Nano Res., 15(2), 141-153. https://doi.org/10.12989/ANR.2023.15.2.141
  102. Xia, J., Jafari, G.S. and Ghoroughi, F. (2024), "New method environment for art design of nanocomposite brick facade of the building", Steel Compos. Struct., 51(5), 499-507. https://doi.org/10.12989/SCS.2024.51.5.499
  103. Xu, G. and Ming, F. (2023), "On dynamic response and economic of sinusoidal porous laminated nanocomposite beams using numerical method", Steel Compos. Struct., 49(3), 349-359. https://doi.org/10.12989/SCS.2023.49.3.349
  104. Yaghoobi, H. and Taheri, F. (2020), "Analytical solution and statistical analysis of buckling capacity of sandwich plates with uniform and non-uniform porous core reinforced with graphene nanoplatelets", Compos. Struct., 252, 112700. https://doi.org/10.1016/j.compstruct.2020.112700
  105. Yahea, H.T. and Majeed, W.I. (2021), "Free vibration of laminated composite plates in thermal environment using a simple four variable plate theory", Compos. Mater. Eng., 3(3), 179-199. https://doi.org/10.12989/cme.2021.3.3.179.
  106. Yang, Z., Liu, A., Yang, J., Fu, J. and Yang, B. (2020), "Dynamic buckling of functionally graded graphene nanoplatelets reinforced composite shallow arches under a step central point load", J. Sound Vib., 465, 115019. https://doi.org/10.1016/j.jsv.2019.11501
  107. Yang, Z., Wu, D., Yang, J., Lai, S.K., Lv, J., Liu, A. and Fu, J. (2021), "Dynamic buckling of rotationally restrained FG porous arches reinforced with graphene nanoplatelets under a uniform step load", Thin Wall. Struct., 166, 108103. https://doi.org/10.1016/j.tws.2021.108103
  108. Yaylaci, E.U., Yaylaci, M., Ozdemir, M.E., Terzi, M. and Ozturk, S. (2023), "Analyzing the mechano-bactericidal effect of nanopatterned surfaces by finite element method and verification with artificial neural networks", Adv. Nano Res., 15(2), 165-174. https://doi.org/10.12989/ANR.2023.15.2.165
  109. Zhao, T., Ma, Y., Zhou, J. and Fu, Y. (2021). "Wave propagation in rotating functionally graded microbeams reinforced by graphene nanoplatelets", Molecules, 26(17), 5150. https://doi.org/10.3390/molecules26175150