DOI QR코드

DOI QR Code

Wave propagation of FG polymer composite nanoplates reinforced with GNPs

  • She, Gui-Lin (College of Mechanical Engineering, Guizhou University)
  • Received : 2020.07.15
  • Accepted : 2020.09.22
  • Published : 2020.10.10

Abstract

This study examines the wave propagation of the functionally graded polymer composite (FG-PC) nanoplates reinforced with graphene nanoplatelets (GNPs) resting on elastic foundations in the framework of the nonlocal strain gradient theory incorporating both stiffness hardening and softening mechanisms of nanostructures. To this end, the material properties are based on the Halpin-Tsai model, and the expressions for the classical and higher-order stresses and strains are consistently derived employing the second-order shear deformation theory. The equations of motion are then consistently derived using Hamilton's principle of variation. These governing equations are solved with the help of Trial function method. Extensive numerical discussions are conducted for wave propagation of the nanoplates and the influences of different parameters, such as the nonlocal parameter, strain gradient parameter, weight fraction of GNPs, uniform and non-uniform distributions of GNPs, elastic foundation parameters as well as wave number.

Keywords

References

  1. 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.
  2. Akgoz, B. and Civalek, O. (2015), "A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory", Acta Mech., 226, 2277-2294. https://doi.org/10.1007/s00707-015-1308-4.
  3. Akgoz, B. and Civalek, O. (2017a), "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.2017.06.039.
  4. 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.
  5. 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
  6. 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.
  7. 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", Euro. J. Mech. A-Solid., 77, 103802. https://doi.org/10.1016/j.euromechsol.2019.103802.
  8. Arefi, M., Bidgoli, 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.
  9. 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.
  10. Barretta, R. and de Sciarra, F.M. (2019), "Variational nonlocal gradient elasticity for nano-beams", Int. J. Eng. Sci., 143, 73-91. https://doi.org/10.1016/j.ijengsci.2019.06.016.
  11. 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.2019.103140.
  12. 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.
  13. Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Sizedependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Euro. Phys. J. Plus, 135, 381. https://doi.org/10.1140/epjp/s13360-020-00385-w.
  14. Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates", Euro. Phys. J. Plus, 133, 151. https://doi.org/10.1140/epjp/i2018-11956-5.
  15. 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.
  16. Ebrahimi, F., et al. (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.
  17. Eltaher, M.A. and Mohamed, N.A. (2020a), "Vibration of nonlocal perforated nanobeams with general boundary conditions", Smart. Struct. Syst., 25(4), 501-514. https://doi.org/10.12989/sss.2020.25.4.501.
  18. Eltaher, M.A. and Abdelrahman, A.A. (2020c), "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.
  19. Eltaher, M.A. and Mohamed, N. (2020d), "Nonlinear stability and vibration of imperfect CNTs by Doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
  20. Eltaher, M.A., Omar, F.A., Abdraboh, A.M., Abdalla, W.S. and Alshorbagy, A.E. (2020b), "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.
  21. 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.
  22. 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.
  23. 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.
  24. Fu, Y., Zhong, J. and Chen, Y. (2014), "Thermal postbuckling analysis of fiber-metal laminated plates including interfacial damage", Compos. Part B-Eng., 56, 358-364. https://doi.org/10.1016/j.compositesb.2013.08.033.
  25. Gao, W., Qin, Z. and Chu, F. (2020), "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerosp. Sci. Technol., 102, 105860.https://doi.org/10.1016/j.ast.2020.105860.
  26. 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.
  27. 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.
  28. 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.
  29. 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.
  30. Heydari, A. (2018), "Exact vibration and buckling analyses of arbitrary gradation of nano-higher order rectangular beam", Steel Compos. Struct., 28(5),589-606. https:// doi.org/10.12989/scs.2018.28.5.589.
  31. Heydari, A. and Shariati, M. (2018), "Buckling analysis of tapered bdfgm nano-beam under variable axial compression resting on elastic medium", Struct. Eng. Mech., 66(6), 737-748. https://doi.org/10.12989/sem.2018.66.6.737.
  32. Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
  33. 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.
  34. Karami, B., Janghorban, M. and Rabczuk, T. (2019), "Analysis of elastic bulk waves in functionally graded triclinic nanoplates using 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.
  35. 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), 1, 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  36. Khdeir, A. and Reddy, J.N. (1999), "Free vibrations of laminated composite plates using second-order shear deformation theory", Comput. Struct., 71, 617-626. https://doi.org/10.1016/S0045-7949(98)00301-0.
  37. 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.
  38. 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.2015.02.001.
  39. Liu, F., Ming, P. and Li, J. (2007), "Ab initio calculation of ideal strength and phonon instability of graphene under tension", Phys. Review B., 76(6), 064120. https://doi.org/10.1103/PhysRevB.76.064120.
  40. Liu, H., Wu, H. and Lyu, Z. (2020), "Nonlinear resonance of FG multilayer beam-type nanocomposites: Effects of graphene nanoplatelet-reinforcement and geometric imperfection", Aerosp. Sci. Technol., 98, 105702. https://doi.org/10.1016/j.ast.2020.105702.
  41. 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.
  42. Malikan, M., Krasheninnikov, M. and Eremeyev, V.A. (2020a), "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.2019.103210.
  43. Malikan, M., Uglov, N.S. and Eremeyev, V.A. (2020b), "On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures", Int. J. Eng. Sci., 157, 103395. https://doi.org/10.1016/j.ijengsci.2020.103395Get.
  44. 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.
  45. Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001.
  46. 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.
  47. 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
  48. 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
  49. 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.
  50. 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. Concrete, 23(4), 295-301. https://doi.org/10.12989/cac.2019.23.4.295.
  51. Uzun, B. and Civalek, O. (2019), "Nonlocal FEM formulation for vibration analysis of nanowires on elastic matrix with different materials", Math. Comput. Appl., 24, UNSP 38. https://doi.org/doi:10.3390/mca24020038.
  52. 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.

Cited by

  1. Axisymmetric vibration analysis of graded porous Mindlin circular plates subjected to thermal environment vol.16, pp.3, 2020, https://doi.org/10.2140/jomms.2021.16.371
  2. Vibration of multilayered functionally graded deep beams under thermal load vol.24, pp.6, 2020, https://doi.org/10.12989/gae.2021.24.6.545
  3. Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position vol.39, pp.1, 2021, https://doi.org/10.12989/scs.2021.39.1.051
  4. Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory vol.39, pp.1, 2020, https://doi.org/10.12989/scs.2021.39.1.095
  5. Finite element based stress and vibration analysis of axially functionally graded rotating beams vol.79, pp.1, 2020, https://doi.org/10.12989/sem.2021.79.1.023
  6. An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells vol.40, pp.2, 2020, https://doi.org/10.12989/scs.2021.40.2.307
  7. Mechanical and thermal buckling analysis of laminated composite plates vol.40, pp.5, 2020, https://doi.org/10.12989/scs.2021.40.5.697