Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A new quasi-3D plate theory for free vibration analysis of advanced composite nanoplates

  • Smain, Bezzina (Deanship for Scientific research, King Abdulaziz University) ;
  • Aicha, Bessaim (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohammed Sid Ahmed, Houari (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Marc, Azab (College of Engineering and Technology, American University of the Middle East)
  • Received : 2021.12.24
  • Accepted : 2022.12.07
  • Published : 2022.12.25
⟨ Previous Next ⟩

Abstract

This paper presents an analytical solution to study the combined effect of non-local and stretching effect on the vibration of advanced functionally graded (FG) nanoplates. A new quasi-3D plate theory is presented; there are only five unknowns and any shear correction factor is used. A new displacement field with a new shear warping function is proposed. The equilibrium equations of the FG nanoplates are obtained using the Hamilton principle and solved numerically using the Navier technique. The material properties of functionally graded nanoplates are presumed to change according to the power-law distribution of ceramic and metal constituents. The numerical results of this work are compared with those of other published results to indicate the accuracy and convergence of this theory. Hence, a profound parameterstudy is also performed to show the influence of many parameters of the functionally graded nanoplates on the free vibration responses is investigated.

Keywords

Acknowledgement

This Project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant no. G: 604-305-1443.The authors, therefore, acknowledge with thanks DSR for technical and financial support.

References

  1. Abdelrahman, A.A., Esen, I., Ozarpa, C. and Eltaher, M.A. (2021a), "Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory", Appl. Mathem. Modelling., 96, 215-235. https://doi.org/10.1016/j.apm.2021.03.008.
  2. Abdelrahman, A.A., Esen, I., Ozarpa, C., Shaltout, R., Eltaher, M. A. and Assie, A.E. (2021b), "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//10.1016/j.apm.2021.03.008
  3. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  4. Ansari, R., Ashrafi, M.A., Pourashraf, T. And Sahmani, S. (2015), "Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory", Acta Astronautica, 109, 42-51. https://doi.org//10.1016/j.actaastro.2014.12.015.
  5. Attia, A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187.
  6. Barati, M.R. (2017), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. http://dx.doi.org/10.12989/sem.2017.64.6.683
  7. Barati, M.R. (2017), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/sem.2017.64.6.683
  8. Barati, M.R. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. http://dx.doi.org/10.12989/sem.2016.60.4.707.
  9. Barati, M.R. and Shahverdi, H. (2017), "An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position", Mech. Adv. Mater. Struct., 24(10), 840-853. http://dx.doi.org/10.1080/15376494.2016.1196788.
  10. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct, 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.
  11. Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Bedia, E. A.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Structures, 15(5), 467-479. https://doi.org/10.12989/scs.2013.15.5.467.
  12. Daikh, A.A., Drai, A., Bensaid, I., Houari, M.S.A. and Tounsi, A. (2021), "On vibration of functionally graded sandwich nanoplates in the thermal environment", J. Sandw. Struct. Mater., 23(6), 2217-2244. https://doi.org/10.1177/1099636220909790.
  13. Daikh, A.A., Houari, M.S.A., Belarbi, M.O., Mohamed, S.A. and Eltaher, M.A. (2022), "Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory", Defence Technol., 18(10), 1778-1809. https://doi.org/10.1016/j.dt.2021.09.011.
  14. Daikh, A.A., Houari, M.S.A., Eltaher, M.A. (2021), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347.
  15. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  16. Elmascri, S., Bessaim, A., Taleb, O., Houari, M.S.A., Mohamed, S., Bernard, F. and Tounsi, A. (2020), "A novel hyperbolic plate theory including stretching effect for free vibration analysis of advanced composite plates in thermal environments", Struct. Eng. Mech., 75(2), 193-209. https://doi.org/10.12989/sem.2020.75.2.193.
  17. Emadi, M., Nejad, M.Z., Ziaee, S. and Hadi, A. (2021), "Buckling analysis of arbitrary two-directional functionally graded nanoplate based on nonlocal elasticity theory using generalized differential quadrature method", Steel Compos. Struct., 39(5), 565-581. http://dx.doi.org/10.12989/scs.2021.39.5.565.
  18. 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.
  19. 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
  20. Esen, I. (2013), "A new finite element for transverse vibration of rectangular thin plates under a moving mass", Finite Element. Anal. Des., 66, 26-35. https://doi.org/10.1016/j.finel.2012.11.005.
  21. Esen, I. (2015), "A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory", Latin Amer. J. Solids Struct., 12, 808-830. https://doi.org/10.1590/1679-78251525.
  22. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2020), "Dynamics analysis of timoshenko perforated microbeams under moving loads", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01212-7.
  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(3), 721-742. doi.org/10.1007/s10999-021-09555-9.
  24. Ghandourah, E.E., Ahmed, H.M., Eltaher, M.A., Attia, M.A. and Abdraboh, A.M. (2021), "Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model", Adv. Nano Res., 11(4), 405-422. https://doi.org/10.12989/anr.2021.11.4.405.
  25. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Bedia, E. A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665.
  26. Hendi, A.A., Eltaher, M.A., Mohamed, S.A., Attia, M.A. and Abdalla, A.W. (2021), "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), 787-803. doi.org/10.12989/scs.2021.41.6.787.
  27. Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/scs.2018.28.1.013.
  28. Houari, T., Bessaim, A., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2018), "Bending analysis of advanced composite plates using a new quasi 3D plate theory", Steel Compos. Struct., 26(5), 557-572. https://doi.org/10.12989/scs.2018.26.5.557.
  29. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", Struct. Eng. Mech., 73(2), 191-207. http://dx.doi.org/10.12989/sem.2020.73.2.191.
  30. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res., 11(1), 1-17. https://doi.org/10.12989/anr.2021.11.1.001.
  31. Lee, Z., Ophus, C., Fischer, L.M., Nelson-Fitzpatrick, N., Westra, K. L., Evoy, S. and Mitlin, D. (2006), "Metallic NEMS components fabricated from nanocomposite Al-Mo films", Nanotechnology, 17(12), 3063. https://doi.org/10.1088/0957-4484/17/12/042.
  32. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  33. Liu, Y., Qin, Z. and Chu, F. (2021), "Nonlinear forced vibrations of functionally graded piezoelectric cylindrical shells under electric-thermo-mechanical loads", Int. J. Mech. Sci., 201, 106474. https://doi.org/10.1016/j.ijmecsci.2021.106474.
  34. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215.
  35. Melaibari, A., Daikh, A.A., Basha, M., Wagih, A., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022), "A dynamic analysis of randomly oriented functionally graded carbon nanotubes/fiber-reinforced composite laminated shells with different geometries", Mathematics, 10(3), 408.  https://doi.org/10.3390/math10030408.
  36. Mindlin, R.D. (1964), "Micro-structure in linear elasticity", Arch. Rational Mech. Anal., 16(1), 51-78. https://doi.org/10.1007/BF00248490.
  37. Mindlin, R.D. (1965), "Second gradient of strain and surface-tension in linear elasticity", Int. J. Solids Struct., 1(4), 417-438. https://doi.org/10.1016/0020-7683(65)90006-5
  38. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.
  39. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012a), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
  40. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012b), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B: Eng., 43(2), 711-725.
  41. Ozarpa, C. and Esen, I. (2020), "Modelling the dynamics of a nanocapillary system with a moving mass using the non-local strain gradient theory", Mathem. Meth. Appl. Sci., https://doi.org/10.1002/mma.6812.
  42. Papargyri-Beskou, S., Tsepoura, K.G., Polyzos, D. and Beskos, D.E. (2003), "Bending and stability analysis of gradient elastic beams", Int. J. Solids Struct., 40(2), 385-400. https://doi.org/10.1016/S0020-7683(02)00522-X.
  43. Pham, Q.H., Nguyen, P.C., Tran, V.K. and Nguyen-Thoi, T. (2021b), "Finite element analysis for functionally graded porous nano-plates resting on elastic foundation", Steel Compos. Struct., 41(2), 149-166. https://doi.org/10.12989/scs.2021.41.2.149.
  44. Pham, Q.H., Tran, V.K., Tran, T.T., Nguyen-Thoi, T. and Nguyen, P.C. (2021a), "A nonlocal quasi-3D theory for thermal free vibration analysis of functionally graded material nanoplates resting on elastic foundation", Case Studies Thermal Eng., 26, 101170. https://doi.org/10.1016/j.csite.2021.101170.
  45. Rahmani, O., Refaeinejad, V. and Hosseini, S.A.H. (2017), "Assessment of various nonlocal higher order theories for the bending and buckling behavior of functionally graded nanobeams", Steel Compos. Struct., 23(3), 339-350. https://doi.org/10.12989/scs.2017.23.3.339.
  46. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)10970207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
  47. Rezaiee-Pajand, M., Masoodi, A.R. and Arabi, E. (2018), "Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element", Steel Compos. Struct., 28(3), 389-401. https://doi.org/10.12989/scs.2018.28.3.389.
  48. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. http://dx.doi.org/10.12989/scs.2018.29.1.053.
  49. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct., 37(1), 27-35. http://dx.doi.org/10.12989/scs.2020.37.1.027.
  50. Singh, P.P. and Azam, M.S. (2021), "Size dependent vibration of embedded functionally graded nanoplate in hygrothermal environment by Rayleigh-Ritz method", Adv. Nano Res., 10(1), 25-42. http://dx.doi.org/10.12989/anr.2021.10.1.025.
  51. Sobhy, M. and Radwan, A.F. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(01), 1750008. https://doi.org/10.1142/S1758825117500089.
  52. Sobhy, M. and Radwan, A.F. (2017), "A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates", Int. J. Appl. Mech., 9(01), 1750008.
  53. Taleb, O., Houari, M.S.A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2018), "A new plate model for vibration response of advanced composite plates in thermal environment", Struct. Eng. Mech., 67(4), 369-383. https://doi.org/10.12989/sem.2018.67.4.369.
  54. Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030.
  55. Thai, H.T., Vo, T.P., Bui, T.Q. and Nguyen, T.K. (2014), "A quasi-3D hyperbolic shear deformation theory for functionally graded plates", Acta Mechanica., 225(3), 951-964. https://doi.org/10.1007/s00707-013-0994-z.
  56. Tong, L.H., Lin, F., Xiang, Y., Shen, H.S. and Lim, C.W. (2021), "Buckling analysis of nanoplates based on a generic third-order plate theory with shear-dependent non-isotropic surface stresses", Compos. Struct., 265, 113708. https://doi.org/10.1016/j.compstruct.2021.113708.
  57. Tu, T.M., Quoc, T.H. and Van Long, N. (2019), "Vibration analysis of functionally graded plates using the eight-unknown higher order shear deformation theory in thermal environments", Aerosp. Sci. Technol., 84, 698-711. https://doi.org/10.1016/j.ast.2018.11.010.
  58. Van Vinh, P. (2022), "Nonlocal free vibration characteristics of power-law and sigmoid functionally graded nanoplates considering variable nonlocal parameter", Physica E: Low-Dimens. Syst. Nanostruct., 135, 114951. https://doi.org/10.1016/j.physe.2021.114951.
  59. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.
  60. Zheng, X., Huang, M., An, D., Zhou, C. and Li, R. (2021), "New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method", Sci. Report. 11(1), 1-16. https://doi.org/10.1038/s41598-021-82326-w.