Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Elastic wave characteristics of graphene nanoplatelets reinforced composite nanoplates

  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Gheisari, Parastoo (School of Mechanical Engineering, Shiraz University) ;
  • Nazemosadat, Seyed Mohammad Reza (Sama Technical and Vocational Training College, Islamic Azad University) ;
  • Akbari, Payam (Department of Civil Engineering, Tehran South Branch, Islamic Azad University) ;
  • Shahsavari, Davood (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Naghizadeh, Matin (Department of Chemistry, Shahid Bahonar University of Kerman)
  • Received : 2019.08.13
  • Accepted : 2020.02.04
  • Published : 2020.06.25
⟨ Previous Next ⟩

Abstract

For the first time, the influence of in-plane magnetic field on wave propagation of Graphene Nano-Platelets (GNPs) polymer composite nanoplates is investigated here. The impact of three- parameter Kerr foundation is also considered. There are two different reinforcement distribution patterns (i.e. uniformly and non-uniformly) while the material properties of the nanoplate are estimated through the Halpin-Tsai model and a rule of mixture. To consider the size-dependent behavior of the structure, Eringen Nonlocal Differential Model (ENDM) is utilized. The equations of wave motion derived based on a higher-order shear deformation refined theory through Hamilton's principle and an analytical technique depending on Taylor series utilized to find the wave frequency as well as phase velocity of the GNPs reinforced nanoplates. A parametric investigation is performed to determine the influence of essential phenomena, such as the nonlocality, GNPs conditions, Kerr foundation parameters, and wave number on the both longitudinal and flexural wave characteristics of GNPs reinforced nanoplates.

Keywords

References

  1. Affdl, J.H. and Kardos, J. (1976), "The Halpin-Tsai equations: a review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  2. Akgoz, B. and Civalek, O. (2014), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Vib. Control., 20(4), 606-616. https://doi.org/10.1177/1077546312463752.
  3. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  4. Arefi, M., Bidgoli, E.M.-R., Dimitri, R. and Tornabene, F. (2018), "Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Aerosp. Sci. Technol., 81 108-117. https://doi.org/10.1016/j.ast.2018.07.036.
  5. Bakhadda, B., Bouiadjra, M.B., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind Struct., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311.
  6. Barati, M.R. and Shahverdi, H. (2017), "Hygro-thermal vibration analysis of graded double-refined-nanoplate systems using hybrid nonlocal stress-strain gradient theory", Compos. Struct., 176 982-995. https://doi.org/10.1016/j.compstruct.2017.06.004.
  7. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech.,. 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  8. Bensaid, I. and Bekhadda, A. (2018), "Thermal stability analysis of temperature dependent inhomogeneous size-dependent nano-scale beams", Adv. Mater. Res. J., 7(1), 363-378. https://doi.org/10.12989/amr.2018.7.1.001.
  9. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., 6(3), 279-298. https://doi.org/10.12989/anr.2018.6.3.279.
  10. Berghouti, H., Adda Bedia, E., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  11. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147.
  12. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  13. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  14. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227.
  15. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661.
  16. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019.
  17. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S. (2019), "Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 191. https://doi.org/10.12989/anr.2019.7.3.191.
  18. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech.., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  19. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech.., 68(6), 721-733. https://doi.org/10.12989/sem.2018.68.6.721.
  20. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel", Earthq. Struct., 16(1), 55-67. https://doi.org/10.12989/eas.2019.16.1.055.
  21. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019). "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  22. Dutta, G., Panda, S.K., Mahapatra, T.R. and Singh, V.K. (2017), "Electro-magneto-elastic response of laminated composite plate: A finite element approach", J. Appl. Comput. Math., 3(3), 2573-2592. https://doi.org/10.1007/s40819-016-0256-6.
  23. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", J. Eng. Sci., 107 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008.
  24. Ebrahimi, F., Barati, M.R. and Zenkour, A.M. (2018), "A new nonlocal elasticity theory with graded nonlocality for thermo-mechanical vibration of FG nanobeams via a nonlocal third-order shear deformation theory", Mech. Adv. Mater. Struct., 25(6), 512-522. https://doi.org/10.1080/15376494.2017.1285458.
  25. Eringen, A.C. (1983), "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.
  26. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  27. Farokhi, H. and Ghayesh, M.H. (2015), "Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory", J. Mech. Sci., 90 133-144. https://doi.org/10.1016/j.ijmecsci.2014.11.002.
  28. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  29. Gao, Y., Xiao, W.-S. and Zhu, H. (2019), "Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method", Struct. Eng. Mech.,. 69(2), 205-219. https://doi.org/10.12989/sem.2019.69.2.205.
  30. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013), "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", J. Eng. Sci., 63 52-60. https://doi.org/10.1016/j.ijengsci.2012.12.001.
  31. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013), "Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams", J. Eng. Sci., 71 1-14. https://doi.org/10.1016/j.ijengsci.2013.04.003.
  32. Ghayesh, M.H. and Farokhi, H. (2018), "Size-dependent internal resonances and modal interactions in nonlinear dynamics of microcantilevers", J. Mech. Mater. Design., 14(1), 127-140. https://doi.org/10.1007/s10999-017-9365-6.
  33. Ghayesh, M.H., Farokhi, H. and Alici, G. (2016), "Size-dependent performance of microgyroscopes", J. Eng. Sci., 100 99-111. https://doi.org/10.1016/j.ijengsci.2015.11.003.
  34. Ghayesh, M.H., Farokhi, H., Gholipour, A., Hussain, S. and Arjomandi, M. (2017), "Resonance responses of geometrically imperfect functionally graded extensible microbeams", J. Comput. Nonlinear Dynam., 12(5), 051002. https://doi.org/10.1115/1.4035214.
  35. Ghayesh, M.H., Farokhi, H., Gholipour, A. and Tavallaeinejad, M. (2018), "Nonlinear oscillations of functionally graded microplates", J. Eng. Sci., 122 56-72. https://doi.org/10.1016/j.ijengsci.2017.03.014.
  36. Gholami, R. and Ansari, R. (2018), "On the Nonlinear Vibrations of Polymer Nanocomposite Rectangular Plates Reinforced by Graphene Nanoplatelets: A Unified Higher-Order Shear Deformable Model", Iranian J. Sci. Technol. Transactions. Mech. Eng.. 1-18. https://doi.org/10.1007/s40997-018-0182-9.
  37. Hosseini, M., Bahaadini, R. and Jamali, B. (2018), "Nonlocal instability of cantilever piezoelectric carbon nanotubes by considering surface effects subjected to axial flow", J. Vib. Control. 24(9), 1809-1825. https://doi.org/10.1177/1077546316669063.
  38. Jawaid, M., Thariq, M. and Saba, N. (2018), Modelling of Damage Processes in Biocomposites, Fibre-Reinforced Composites and Hybrid Composites, Woodhead Publishing. https://doi.org/10.1016/C2016-0-04450-9.
  39. Kaghazian, A., Hajnayeb, A. and Foruzande, H. (2017), "Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory", Struct. Eng. Mech.,. 61(5), 617-624. https://doi.org/10.12989/sem.2017.61.5.617.
  40. Kar, V., Panda, S., Tripathy, P., Jayakrishnan, K., Rajesh, M., Karakoti, A. and Manikandan, M. (2019), Deformation Characteristics of Functionally Graded Composite Panels Using Finite Element Approximation, Elsevier, Germany. https://doi.org/10.1016/B978-0-08-102289-4.00012-6.
  41. Karami, B., Janghorban, M. and Li, L. (2018), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica. 143 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011.
  42. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/sem.2019.69.5.487.
  43. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., 25(3), 361-374. https://doi.org/10.12989/scs.2017.25.3.361.
  44. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  45. Karami, B., Janghorban, M. and Tounsi, A. (2018), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin Wall. Struct., 129 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  46. Karami, B., Janghorban, M. and Tounsi, A. (2019), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  47. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143.
  48. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018), "Wave dispersion of mounted graphene with initial stress", Thin Wall. Struct., 122 102-111. https://doi.org/10.1016/j.tws.2017.10.004.
  49. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", J. Mech. Sci., 156 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  50. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.
  51. Kocaturk, T. and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., 46(3), 417-431. https://doi.org/10.12989/sem.2013.46.3.417.
  52. Li, L. and Hu, Y. (2017), "Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory", Compos. Struct., 172 242-250. https://doi.org/10.1016/j.compstruct.2017.03.097.
  53. Liu, F., Ming, P. and Li, J. (2007), "Ab initio calculation of ideal strength and phonon instability of graphene under tension", Physical Review B. 76(6), 064120. https://doi.org/10.1103/PhysRevB.76.064120.
  54. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577.
  55. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  56. Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519.
  57. Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038.
  58. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181. https://doi.org/10.12989/anr.2019.7.3.181.
  59. Mehar, K. and Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B Eng., 167 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058.
  60. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002.
  61. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandwich Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  62. Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ", Compos. Part B Eng., 114 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067.
  63. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397.
  64. Papargyri-Beskou, S., Polyzos, D. and Beskos, D. (2009), "Wave dispersion in gradient elastic solids and structures: a unified treatment", J. Solids Struct.,46(21), 3751-3759. https://doi.org/10.1016/j.ijsolstr.2009.05.002.
  65. Rad, A.B. (2015), "Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation", Appl. Math. Comput., 256 276-298. https://doi.org/10.1016/j.amc.2015.01.026.
  66. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.-Z. and Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano., 3(12), 3884-3890. https://pubs.acs.org/doi/abs/10.1021/nn9010472.
  67. Rahmani, O., Deyhim, S., Hosseini, S. and Hossein, A. (2018), "Size dependent bending analysis of micro/nano sandwich structures based on a nonlocal high order theory", Steel Compos. Struct., 27(3), 371-388. https://doi.org/10.12989/scs.2018.27.3.371.
  68. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865. https://doi.org/10.12989/scs.2019.33.6.865.
  69. Romano, G. and Barretta, R. (2017), "Nonlocal elasticity in nanobeams: the stress-driven integral model", J. Eng. Sci., 115, 14-27. https://doi.org/10.1016/j.ijengsci.2017.03.002.
  70. Romano, G., Barretta, R., Diaco, M. and de Sciarra, F.M. (2017), "Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams", J. Mech. Sci., 121, 151-156. https://doi.org/10.1016/j.ijmecsci.2016.10.036.
  71. Sahmani, 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.
  72. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets", Mater. Res. Express.,5(4), 045048. https://orcid.org/0000-0003-4129-4554. https://doi.org/10.1088/2053-1591/aabdbb
  73. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazilian Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0.
  74. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express.,4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89.
  75. Song, M., Kitipornchai, S. and Yang, J. (2017), "Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Struct., 159, 579-588. https://doi.org/10.1016/j.compstruct.2016.09.070.
  76. 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.
  77. Wang, L. and Zheng, S. (2018), "Nonlinear analysis of 0-3 polarized PLZT microplate based on the new modified couple stress theory", Physica E: Low-dimensional Syst. Nanostruct.., 96, 94-101. https://doi.org/10.1016/j.physe.2017.10.001.
  78. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015.
  79. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065.
  80. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B Eng., 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  81. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  82. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. https://doi.org/10.12989/sem.2015.54.4.693.

Cited by

  1. Elastic wave phenomenon of nanobeams including thickness stretching effect vol.10, pp.3, 2020, https://doi.org/10.12989/anr.2021.10.3.271
  2. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2020, https://doi.org/10.12989/scs.2021.40.3.355
  3. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2020, https://doi.org/10.12989/anr.2021.11.2.115