DOI QR코드

DOI QR Code

Computational continuum modelling to analysis the dynamic and static stability of a cantilever nano-scale system

  • Jiangjiang, Li (Social Science Foundation Department, Zhejiang College of Security Technology)
  • Received : 2022.12.11
  • Accepted : 2023.01.25
  • Published : 2023.01.25

Abstract

Calculating size-dependent mechanical properties of the nano-scale materials usually involves cumbersome numerical and theoretical works. In this paper, we aim to present a closed-form relation to calculate the length-dependent Young's modulus of carbon nanotubes (CNTs) based on nonlocal elasticity theory. In this regard, a single wall carbon nanotube (SWCNT) is considered as a rod structure and the governing nonlocal equations are developed under uniaxial tensile load. The equations are solved using analytical methods and strain distribution, total displacement and the size-dependent equivalent Young's modulus are obtained. Further, the results are compared with the molecular dynamics results from the literature. The outcome indicates that the calculated relations are coincident with the molecular dynamics results.

Keywords

References

  1. Adamian, A., Safari, K.H., Sheikholeslami, M., Habibi, M., Al-Furjan, M. and Chen, G. (2020), "Critical temperature and frequency characteristics of gpls-reinforced composite doubly curved panel", Appl. Sci., 10(9), 3251. https://doi.org/10.3390/app10093251.
  2. Al-Furjan, M., Dehini, R., Khorami, M., Habibi, M. and won Jung, D. (2020a), "On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory", Compos. Struct., 112990. https://doi.org/10.1016/j.compstruct.2020.112990.
  3. Al-Furjan, M., Fereidouni, M., Habibi, M., Abd Ali, R., Ni, J. and Safarpour, M. (2020b), "Influence of inplane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01177-7.
  4. Al-Furjan, M., Fereidouni, M., Sedghiyan, D., Habibi, M. and won Jung, D. (2020c), "Three-dimensional frequency response of the CNT-Carbon-Fiber reinforced laminated circular/annular plates under initially stresses", Compos. Struct., 113146. https://doi.org/10.1016/j.compstruct.2020.113146.
  5. Al-Furjan, M., Habibi, M., won Jung, D. and Safarpour, H. (2020d), "Vibrational characteristics of a higher-order laminated composite viscoelastic annular microplate via modified couple stress theory", Compos. Struct., 113152. https://doi.org/10.1016/j.compstruct.2020.113152.
  6. Al-Furjan, M., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2020e), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Semi-numerical and finite element modeling", Thin Wall. Struct., 107242. https://doi.org/10.1016/j.tws.2020.107242.
  7. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H. and Jung, D.W. (2020f), "Frequency and critical angular velocity characteristics of rotary laminated cantilever microdisk via two-dimensional analysis", Thin Wall. Struct., 157, 107111. https://doi.org/10.1016/j.tws.2020.107111.
  8. Al-Furjan, M.S.H., Habibi, M., Jung, D.w., Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2020g), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., 38(2), 1679-1696. https://doi.org/10.1007/s00366-020-01130-8.
  9. Al-Furjan, M.S.H., Habibi, M., Ni, J., Jung, D.w. and Tounsi, A. (2020h), "Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01200-x.
  10. Al-Furjan, M.S.H., Habibi, M., rahimi, A., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020i), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01144-2.
  11. Al-Furjan, M.S.H., hatami, A., Habibi, M., Shan, L. and Tounsi, A. (2021), "On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method", Compos. Struct., 257, 113150. https://doi.org/10.1016/j.compstruct.2020.113150.
  12. Alipour, M., Torabi, M.A., Sareban, M., Lashini, H., Sadeghi, E., Fazaeli, A., Habibi, M. and Hashemi, R. (2020), "Finite element and experimental method for analyzing the effects of martensite morphologies on the formability of DP steels", Mech. Based Des. Struct., 48(5), 525-541. https://doi.org/10.1080/15397734.2019.1633343.
  13. Altan, S.B. (1989), "Uniqueness of initial-boundary value problems in nonlocal elasticity", Int. J. Solid Struct., 25(11), 1271-1278. https://doi.org/10.1016/0020-7683(89)90091-7.
  14. Amelirad, O. and Assempour, A. (2019), "Experimental and crystal plasticity evaluation of grain size effect on formability of austenitic stainless steel sheets", J. Manuf. Proc., 47, 310-323. https://doi.org/10.1016/j.jmapro.2019.09.035.
  15. Amelirad, O. and Assempour, A. (2021), "Coupled continuum damage mechanics and crystal plasticity model and its application in damage evolution in polycrystalline aggregates", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-021-01346-2.
  16. Anandatheertha, S., Naik, G.N., Gopalakrishnan, S. and Rao, P.S. (2010), "High accuracy curve fits for chirality, length and diameter dependent initial modulus of single walled carbon nanotubes", Physica E, 43(1), 252-255. https://doi.org/10.1016/j.physe.2010.07.018
  17. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2021), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01382-y.
  18. Asgharnejad Lamraski, M.B., Naikoo, G.A., Zamani Pedram, M., Sohani, A., Hoseinzadeh, S. and Moradi, H. (2022), "Thermodynamic modeling of several alcohol-hydrocarbon binary mixtures at low to moderate conditions", J. Mol. Liq., 346, 117924. https://doi.org/10.1016/j.molliq.2021.117924.
  19. Aydogdu, M., Arda, M. and Filiz, S. (2018), "Vibration of axially functionally graded nano rods and beams with a variable nonlocal parameter", Adv. Nano Res., 6(3), 257. https://doi.org/10.12989/anr.2018.6.3.257.
  20. Bai, Y., Alzahrani, B., Baharom, S. and Habibi, M. (2020), "Semi-numerical simulation for vibrational responses of the viscoelastic imperfect annular system with honeycomb core under residual pressure", Eng. Comput., 1-26. https://doi.org/10.1007/s00366-020-01191-9.
  21. Bellal, M., Hebali, H., Heireche, H., Bousahla, A.A., Tounsi, A., Bourada, F., Mahmoud, S., Bedia, E. and Tounsi, A. (2020), "Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model", Steel Compos. Struct., 34(5), 643-655. https://doi.org/10.12989/scs.2020.34.5.643.
  22. Bendaida, M., Bousahla, A.A., Mouffoki, A., Heireche, H., Bourada, F., Tounsi, A., Benachour, A., Tounsi, A. and Hussain, M. (2022), "Dynamic properties of nonlocal temperature-dependent fg nanobeams under various thermal environments", Transp. Porous Med., 142(1), 187-208. https://doi.org/10.1007/s11242-021-01666-3.
  23. Bendenia, N., Zidour, M., Bousahla Abdelmoumen, A., Bourada, F., Tounsi, A., Benrahou Kouider, H., Bedia, E.A.A., Mahmoud, S.R. and Tounsi, A. (2020), "Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation", Comput. Concr., 26(3), 213-226. https://doi.org/10.12989/CAC.2020.26.3.213.
  24. Bouafia, H., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Hussain, M. (2021), "Natural frequencies of FGM nanoplates embedded in an elastic medium", Adv. Nano Res., 11(3), 239-249. https://doi.org/10.12989/anr.2021.11.3.239.
  25. Bourada, F., Bousahla Abdelmoumen, A., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou Kouider, H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concr., 25(6), 485-495. https://doi.org/10.12989/CAC.2020.25.6.485.
  26. Bousahla Abdelmoumen, A., Bourada, F., Mahmoud, S.R., Tounsi, A., Algarni, A., Bedia, E.A.A. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concr., 25(2), 155-166. https://doi.org/10.12989/CAC.2020.25.2.155.
  27. 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
  28. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  29. Chang, T. and Gao, H. (2003), "Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model", J. Mech. Phys. Solids, 51(6), 1059-1074 10.1016/s0022-5096(03)00006-1.
  30. Chen, F., Chen, J., Duan, R., Habibi, M. and Khadimallah, M.A. (2022), "Investigation on dynamic stability and aeroelastic characteristics of composite curved pipes with any yawed angle", Compos. Struct., 115195. https://doi.org/10.1016/j.compstruct.2022.115195.
  31. Cheshmeh, E., Karbon, M., Eyvazian, A., Jung, D.w., Habibi, M. and Safarpour, M. (2020), "Buckling and vibration analysis of FG-CNTRC plate subjected to thermo-mechanical load based on higher order shear deformation theory", Mech. Based Des. Struct., 1-24. https://doi.org/10.1080/15397734.2020.1744005.
  32. Dai, Z., Jiang, Z., Zhang, L. and Habibi, M. (2021a), "Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell", Adv. Nano Res., 10(2), 175-189. https://doi.org/10.12989/anr.2021.10.2.175.
  33. Dai, Z., Zhang, L., Bolandi, S.Y. and Habibi, M. (2021b), "On the vibrations of the non-polynomial viscoelastic composite open-type shell under residual stresses", Compos. Struct., 113599. https://doi.org/10.1016/j.compstruct.2021.113599.
  34. Dong, Y., Gao, Y., Zhu, Q., Moradi, Z. and Safa, M. (2022), "TE-GDQE implementation to investigate the vibration of FG composite conical shells considering a frequency controller solid ring", Eng. Anal. Bound. Elem., 138, 95-107. https://doi.org/10.1016/j.enganabound.2022.01.017.
  35. Ebrahimi, F., Dabbagh, A., Rabczuk, T. and Tornabene, F. (2019a), "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme", Adv. Nano Res., 7(2), 135. https://doi.org/10.12989/anr.2019.7.2.135.
  36. Ebrahimi, F., Habibi, M. and Safarpour, H. (2019b), "On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell", Eng. Comput., 35(4), 1375-1389. https://doi.org/10.1007/s00366-018-0669-4.
  37. Ebrahimi, F., Hajilak, Z.E., Habibi, M. and Safarpour, H. (2019c), "Buckling and vibration characteristics of a carbon nanotube-reinforced spinning cantilever cylindrical 3D shell conveying viscous fluid flow and carrying spring-mass systems under various temperature distributions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(13), 4590-4605. https://doi.org/10.1177/0954406219832323.
  38. Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2020a), "Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell", Microsyst. Technol., 26(2), 461-473. https://doi.org/10.1007/s00542-019-04542-9.
  39. Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2019d), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Wave Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1694729.
  40. Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020b), "Frequency characteristics of a GPL-reinforced composite microdisk coupled with a piezoelectric layer", Eur. Phys. J. Plus, 135(2), 144. https://doi.org/10.1140/epjp/s13360-020-00217-x.
  41. Eringen, A.C. (1972), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-x.
  42. Eringen, A.C. (2002), Nonlocal continuum field theory, Springer-Verlag, New York, U.S.A.
  43. Esmailpoor Hajilak, Z., Pourghader, J., Hashemabadi, D., Sharifi Bagh, F., Habibi, M. and Safarpour, H. (2019), "Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory", Mech. Based Des. Struct., 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743.
  44. Failla, G., Santini, A. and Zingales, M. (2010), "Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay", Mech. Res. Commun., 37(1), 13-21. https://doi.org/10.1016/j.mechrescom.2009.09.006.
  45. Fan, L., Huang, Y., Ji, D., Moradi, Z., Safa, M. and Amine Khadimallah, M. (2022), "Interaction of angular velocity and temperature rise in the thermo-inertia bifurcation buckling of FG laminated nanocomposite annular plates", Eng. Struct., 265, 114518. https://doi.org/10.1016/j.engstruct.2022.114518.
  46. Fazaeli, A., Habibi, M. and Ekrami, A.a. (2016), "Experimental and finite element comparison of mechanical properties and formability of dual phase steel and ferrite - pearlite steel with the same chemical composition", Metall. Eng., 19(2), 84-93. https://doi.org/10.22076/me.2017.41458.1064.
  47. Ghazanfari, A., Soleimani, S.S., Keshavarzzadeh, M., Habibi, M., Assempuor, A. and Hashemi, R. (2020), "Prediction of FLD for sheet metal by considering through-thickness shear stresses", Mech. Based Des. Struct., 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.
  48. Guo, J., Baharvand, A., Tazeddinova, D., Habibi, M., Safarpour, H., Roco-Videla, A. and Selmi, A. (2021a), "An intelligent computer method for vibration responses of the spinning multi-layer symmetric nanosystem using multi-physics modeling", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01433-4.
  49. Guo, Y., Mi, H. and Habibi, M. (2021b), "Electromechanical energy absorption, resonance frequency, and low-velocity impact analysis of the piezoelectric doubly curved system", Mech. Syst. Signal Proc., 157, 107723. https://doi.org/10.1016/j.ymssp.2021.107723.
  50. Habibi, M., Darabi, R., Sa, J.C.d. and Reis, A. (2021), "An innovation in finite element simulation via crystal plasticity assessment of grain morphology effect on sheet metal formability", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 235(8), 1937-1951. https://doi.org/10.1177/14644207211024686.
  51. Habibi, M., Ghazanfari, A., Assempour, A., Naghdabadi, R. and Hashemi, R. (2017), "Determination of forming limit diagram using two modified finite element models", Mech. Eng., 48(4), 141-144. https://doi.org/10.22060/MEJ.2016.664.
  52. Habibi, M., Hashemabadi, D. and Safarpour, H. (2019a), "Vibration analysis of a high-speed rotating GPLRC nanostructure coupled with a piezoelectric actuator", Eur. Phys. J. Plus, 134(6), 307. https://doi.org/10.1140/epjp/i2019-12742-7.
  53. Habibi, M., Hashemi, R., Ghazanfari, A., Naghdabadi, R. and Assempour, A. (2018a), "Forming limit diagrams by including the M-K model in finite element simulation considering the effect of bending", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 232(8), 625-636. https://doi.org/10.1177/1464420716642258.
  54. Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Perform., 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1
  55. Habibi, M., Hashemi, R., Tafti, M.F. and Assempour, A. (2018b), "Experimental investigation of mechanical properties, formability and forming limit diagrams for tailor-welded blanks produced by friction stir welding", J. Manuf. Proc., 31, 310-323. https://doi.org/10.1016/j.jmapro.2017.11.009.
  56. Habibi, M., Mohammadgholiha, M. and Safarpour, H. (2019b), "Wave propagation characteristics of the electrically GNP-reinforced nanocomposite cylindrical shell", J. Brazil. Soc. Mech. Sci. Eng., 41(5), 221. https://doi.org/10.1007/s40430-019-1715-x.
  57. Habibi, M., Mohammadi, A., Safarpour, H. and Ghadiri, M. (2019c), "Effect of porosity on buckling and vibrational characteristics of the imperfect GPLRC composite nanoshell", Mech. Based Des. Struct., 1-30. https://doi.org/10.1080/15397734.2019.1701490.
  58. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019d), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct., 1-19. https://doi.org/10.1080/15397734.2019.1697932.
  59. Habibi, M., Safarpour, M. and Safarpour, H. (2020), "Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods", Mech. Based Des. Struct., 1-22. https://doi.org/10.1080/15397734.2020.1779086.
  60. Habibi, M., Taghdir, A. and Safarpour, H. (2019e), "Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets", J. Brazil. Soc. Mech. Sci. Eng., 175, 107125. https://doi.org/10.1016/j.compositesb.2019.107125.
  61. Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Wave Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1662968.
  62. Heidari, F., Taheri, K., Sheybani, M., Janghorban, M. and Tounsi, A. (2021), "On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes", Steel Compos. Struct., 38(5), 533-545. https://doi.org/10.12989/SCS.2021.38.5.533.
  63. Hosseini, M., Gorgani, H.H., Shishesaz, M. and Hadi, A. (2017), "Size-dependent stress analysis of single-wall carbon nanotube based on strain gradient theory", Int. J. Appl. Mech., 9(6), 1750087. https://doi.org/10.1142/s1758825117500879.
  64. Hosseini, M., Hadi, A., Malekshahi, A. and Shishesaz, M. (2018), "A review of size-dependent elasticity for nanostructures", Journal of Computational Applied Mechanics. 49(1), 197-211.
  65. Hou, F., Wu, S., Moradi, Z. and Shafiei, N. (2021), "The computational modeling for the static analysis of axially functionally graded micro-cylindrical imperfect beam applying the computer simulation", Eng. Comput., 1-19. https://doi.org/10.1007/s00366-021-01456-x.
  66. Huang, X., Hao, H., Oslub, K., Habibi, M. and Tounsi, A. (2021a), "Dynamic stability/instability simulation of the rotary size-dependent functionally graded microsystem", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01399-3.
  67. Huang, X., Zhang, Y., Moradi, Z. and Shafiei, N. (2021b), "Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform micro-tube", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-021-01395-7.
  68. Huang, X., Zhu, Y., Vafaei, P., Moradi, Z. and Davoudi, M. (2021c), "An iterative simulation algorithm for large oscillation of the applicable 2D-electrical system on a complex nonlinear substrate", Eng. Comput., 1-13. https://doi.org/10.1007/s00366-021-01320-y.
  69. Huang, Y., Karami, B., Shahsavari, D. and Tounsi, A. (2021d), "Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels", Arch. Civil Mech. Eng., 21(4), 139. https://doi.org/10.1007/s43452-021-00291-7.
  70. Jiao, J., Ghoreishi, S.-m., Moradi, Z. and Oslub, K. (2021), "Coupled particle swarm optimization method with genetic algorithm for the static-dynamic performance of the magneto-electro-elastic nanosystem", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-021-01391-x.
  71. Kong, F., Dong, F., Duan, M., Habibi, M., Safarpour, H. and Tounsi, A. (2022), "On the vibrations of the Electrorheological sandwich disk with composite face sheets considering pre and post-yield regions", Thin Wall. Struct., 179, 109631. https://doi.org/10.1016/j.tws.2022.109631.
  72. 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.
  73. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., 33(1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.
  74. Lata, P. and Singh, S. (2021), "Effects due to two temperature and hall current in a nonlocal isotropic magneto-thermoelastic solid with memory dependent derivatives", Coupled Syst. Mech., 10(4), 351-369. https://doi.org/10.12989/csm.2021.10.4.351.
  75. Lata, P. and Singh, S. (2022), "Rayleigh wave propagation in a nonlocal isotropic magneto-thermoelastic solid with multi-dual-phase lag heat transfer", Int. J. Geomath., 13(1), 5 https://doi.org/10.1007/s13137-022-00195-5.
  76. Lee, K., Lukic, B., Magrez, A., Seo, J.W., Briggs, G.A.D., Kulik, A.J. and Forro, L. (2007), "Diameter-dependent elastic modulus supports the metastable-catalyst growth of carbon nanotubes", Nano Lett., 7(6), 1598-1602. https://doi.org/10.1021/nl070502b.
  77. Li, C. and Chou, T.-W. (2003), "A structural mechanics approach for the analysis of carbon nanotubes", Int. J. Solid Struct., 40, 2487-2499. https://doi.org/10.1016/S0020-7683(03)00056-8.
  78. Li, J., Tang, F. and Habibi, M. (2020a), "Bi-directional thermal buckling and resonance frequency characteristics of a GNP-reinforced composite nanostructure", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01110-y.
  79. Li, Y., Li, S., Guo, K., Fang, X. and Habibi, M. (2020b), "On the modeling of bending responses of graphene-reinforced higher order annular plate via two-dimensional continuum mechanics approach", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01166-w.
  80. Lingamdinne, L.P., Amelirad, O., Koduru, J.R., Karri, R.R., Chang, Y.-Y., Dehghani, M.H. and Mubarak, N.M. (2023), "Functionalized bentonite for removal of Pb(II) and As(V) from surface water: Predicting capability and mechanism using artificial neural network", J. Water Proc. Eng., 51, 103386. https://doi.org/10.1016/j.jwpe.2022.103386.
  81. Liu, H., Shen, S., Oslub, K., Habibi, M. and Safarpour, H. (2021a), "Amplitude motion and frequency simulation of a composite viscoelastic microsystem within modified couple stress elasticity", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-021-01316-8.
  82. Liu, H., Zhao, Y., Pishbin, M., Habibi, M., Bashir, M. and Issakhov, A. (2021b), "A comprehensive mathematical simulation of the composite size-dependent rotary 3D microsystem via two-dimensional generalized differential quadrature method", Eng. Comput., 1-16. https://doi.org/10.1007/s00366-021-01419-2.
  83. Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021c), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-021-01454-z.
  84. Liu, Z., Su, S., Xi, D. and Habibi, M. (2020a), "Vibrational responses of a MHC viscoelastic thick annular plate in thermal environment using GDQ method", Mech. Based Des. Struct., 1-26. https://doi.org/10.1080/15397734.2020.1784201.
  85. Liu, Z., Wu, X., Yu, M. and Habibi, M. (2020b), "Large-amplitude dynamical behavior of multilayer graphene platelets reinforced nanocomposite annular plate under thermo-mechanical loadings", Mech. Based Des. Struct., 1-25. https://doi.org/10.1080/15397734.2020.1815544.
  86. Lori, E.S., Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020), "The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-01004-z.
  87. Luo, J., Song, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022a), "Effect of simultaneous compressive and inertia loads on the bifurcation stability of shear deformable functionally graded annular fabrications reinforced with graphenes", Eur. J. Mech. A Solids, 104581. https://doi.org/10.1016/j.euromechsol.2022.104581.
  88. Luo, J., Wu, S., Hou, S., Moradi, Z., Habibi, M. and Khadimallah, M.A. (2022b), "Thermally nonlinear thermoelasticity of a one-dimensional finite domain based on the finite strain concept", Eur. J. Mech. A Solids, 104726. https://doi.org/10.1016/j.euromechsol.2022.104726.
  89. Ma, L., Liu, X. and Moradi, Z. "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 1-25. https://doi.org/10.1007/s00366-020-01210-9.
  90. Matouk, H., Bousahla Abdelmoumen, A., Heireche, H., Bourada, F., Bedia, E.A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. and Benrahou, K.H. (2020), "Investigation on hygro-thermal vibration of P-FG and symmetric S-FG nanobeam using integral Timoshenko beam theory", Adv. Nano Res., 8(4), 293-305. https://doi.org/10.12989/anr.2020.8.4.293.
  91. Michael, M., Meyyazhagan, A., Velayudhannair, K., Pappuswamy, M., Maria, A., Xavier, V., Balasubramanian, B., Baskaran, R., Kamyab, H. and Vasseghian, Y. (2022), "The content of heavy metals in cigarettes and the impact of their leachates on the aquatic ecosystem", Sustainability, 14(8), 4752. https://doi.org/10.3390/su14084752.
  92. Moayedi, H., Aliakbarlou, H., Jebeli, M., Noormohammadiarani, O., Habibi, M., Safarpour, H. and Foong, L. (2020a), "Thermal buckling responses of a graphene reinforced composite micropanel structure", Int. J. Appl. Mech., 12(1), 2050010. https://doi.org/10.1142/S1758825120500106.
  93. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H. and Foong, L.K. (2020b), "Application of nonlocal strain-stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell", Eng. Comput., 1-16. https://doi.org/10.1007/s00366-020-01002-1.
  94. Moayedi, H., Habibi, M., Safarpour, H., Safarpour, M. and Foong, L. (2019), "Buckling and frequency responses of a graphene nanoplatelet reinforced composite microdisk", Int. J. Appl. Mech., 11(10), 1950102. https://doi.org/10.1142/S1758825119501023.
  95. Mohammadgholiha, M., Shokrgozar, A., Habibi, M. and Safarpour, H. (2019), "Buckling and frequency analysis of the nonlocal strain-stress gradient shell reinforced with graphene nanoplatelets", J. Vib. Control, 25(19-20), 2627-2640. https://doi.org/10.1177/1077546319863251.
  96. Mohammadi, A., Lashini, H., Habibi, M. and Safarpour, H. (2019), "Influence of viscoelastic foundation on dynamic behaviour of the double walled cylindrical inhomogeneous micro shell using MCST and with the aid of GDQM", J. Solid Mech., 11(2), 440-453 10.22034/JSM.2019.665264.
  97. Moradi, H., Atashi, P., Amelirad, O., Yang, J.K., Chang, Y.Y. and Kamranifard, T. (2022a), "Machine learning modeling and DOE-assisted optimization in synthesis of nanosilica particles via Stober method", Adv. Nano Res., 12(4), 387-403. https://doi.org/10.12989/anr.2022.12.4.387
  98. Moradi, H., Kim, D.S., Kim, S.H., Chang, Y.Y., Yang, J.K., Choi, E.H. and Kamranifard, T. (2022b), "Experimental and numerical study on diazinon removal using plasma bubble column reactor: Modeling, kinetics, mechanisms, and degradation products", J. Environ. Chem. Eng., 10(5), 108291. https://doi.org/10.1016/j.jece.2022.108291.
  99. Moradi, Z., Davoudi, M., Ebrahimi, F. and Ehyaei, A.F. (2021), "Intelligent wave dispersion control of an inhomogeneous micro-shell using a proportional-derivative smart controller", Wave Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1926572.
  100. Najaafi, N., Jamali, M., Habibi, M., Sadeghi, S., Jung, D.w. and Nabipour, N. (2020), "Dynamic instability responses of the substructure living biological cells in the cytoplasm environment using stress-strain size-dependent theory", J. Biomol. Struct. Dyn., 1-12. https://doi.org/10.1080/07391102.2020.1751297.
  101. Naumov, A.V., Tsyboulski, D.A., Bachilo, S.M. and Weisman, R.B. (2013), "Length-dependent optical properties of single-walled carbon nanotube samples", Chem, Phys., 422, 255-263. https://doi.org/10.1016/j.chemphys.2012.12.033
  102. Oyarhossein, M.A., Alizadeh, A.a., Habibi, M., Makkiabadi, M., Daman, M., Safarpour, H. and Jung, D.W. (2020), "Dynamic response of the nonlocal strain-stress gradient in laminated polymer composites microtubes", Sci. Rep., 10(1), 1-19. https://doi.org/10.1038/s41598-020-61855-w.
  103. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41(3-5), 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  104. Pham, Q.H., Nguyen, P.C., Tran, V.K. and Nguyen-Thoi, T. (2021), "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.
  105. Pisano, A.A. and Fuschi, P. (2003), "Closed form solution for a nonlocal elastic bar in tension", Int. J. Solid Struct., 40(1), 13-23 https://doi.org/10.1016/s0020-7683(02)00547-4.
  106. Polizzotto, C. (2001), "Nonlocal elasticity and related variational principles", Int. J. Solid Struct., 38(42-43), 7359-7380. https://doi.org/10.1016/S0020-7683(01)00039-7
  107. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of Porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041.
  108. Ranjbartoreh, A. and Wang, G. (2010), "Molecular dynamic investigation of length dependency of single-walled carbon nanotube", Physica E, 43(1), 202-206. https://doi.org/10.1016/j.physe.2010.07.013
  109. Rao, P.S., Anandatheertha, S., Naik, G.N. and Gopalakrishnan, S. (2015), "Estimation of mechanical properties of single wall carbon nanotubes using molecular mechanics approach", Sadhana, 40(4), 1301-1311. https://doi.org/10.1007/s12046-015-0367-5
  110. Rouabhia, A., Chikh, A., Bousahla, A.A., Bourada, F., Heireche, H., Tounsi, A., Kouider Halim, B., Tounsi, A. and Al-Zahrani, M.M. (2020), "Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory", Steel Compos. Struct., 37(6), 695-709. https://doi.org/10.12989/scs.2020.37.6.695.
  111. Safarpour, H., Ghanizadeh, S.A. and Habibi, M. (2018), "Wave propagation characteristics of a cylindrical laminated composite nanoshell in thermal environment based on the nonlocal strain gradient theory", Eur. Phys. J. Plus, 133(12), 532. https://doi.org/10.1140/epjp/i2018-12385-2.
  112. Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019a), "A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation", Int. J. Mech. Mater. Des., 15(3), 569-583. https://doi.org/10.1007/s10999-018-9431-8
  113. Safarpour, H., Pourghader, J. and Habibi, M. (2019b), "Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator", J. Vib. Control, 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465.
  114. Safarpour, M., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-00949-5.
  115. Shao, Y., Zhao, Y., Gao, J. and Habibi, M. (2021), "Energy absorption of the strengthened viscoelastic multi-curved composite panel under friction force", Arch. Civil Mech. Eng., 21(4), 1-29. https://doi.org/10.1007/s43452-021-00279-3.
  116. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2020a), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-01024-9.
  117. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020b), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Materials, 13(7), 1707. https://doi.org/10.3390/ma13071707.
  118. Shariati, A., Mohammad-Sedighi, H., Zur, K.K., Habibi, M. and Safa, M. (2020c), "Stability and dynamics of viscoelastic moving rayleigh beams with an asymmetrical distribution of material parameters", Symmetry, 12(4), 586. https://doi.org/10.3390/sym12040586.
  119. Shariati, M., Azar, S.M., Arjomand, M.-A., Tehrani, H.S., Daei, M. and Safa, M. (2020d), "Evaluating the impacts of using piles and geosynthetics in reducing the settlement of fine-grained soils under static load", Geomech. Eng., 20(2), 87-101. https://doi.org/10.12989/gae.2020.20.2.087.
  120. Shariati, M., Davoodnabi, S.M., Toghroli, A., Kong, Z. and Shariati, A. (2021a), "Hybridization of metaheuristic algorithms with adaptive neuro-fuzzy inference system to predict load-slip behavior of angle shear connectors at elevated temperatures", Compos. Struct., 114524. https://doi.org/10.1016/j.compstruct.2021.114524.
  121. Shariati, M., Faegh, S.S., Mehrabi, P., Bahavarnia, S., Zandi, Y., Masoom, D.R., Toghroli, A., Trung, N.-T. and Salih, M.N. (2019), "Numerical study on the structural performance of corrugated low yield point steel plate shear walls with circular openings", Steel Compos. Struct., 33(4), 569-581. https://doi.org/10.12989/scs.2019.33.4.569.
  122. Shariati, M., Ghorbani, M., Naghipour, M., Alinejad, N. and Toghroli, A. (2020e), "The effect of RBS connection on energy absorption in tall buildings with braced tube frame system", Steel Compos. Struct., 34(3), 393-407. https://doi.org/10.12989/scs.2020.34.3.393.
  123. Shariati, M., Lagzian, M., Maleki, S., Shariati, A. and Trung, N.T. (2020f), "Evaluation of seismic performance factors for tension-only braced frames", Steel Compos. Struct., 35(4), 599-609. https://doi.org/10.12989/scs.2020.35.4.599.
  124. Shariati, M., Mafipour, M.S., Ghahremani, B., Azarhomayun, F., Ahmadi, M., Trung, N.T. and Shariati, A. (2020g), "A novel hybrid extreme learning machine-grey wolf optimizer (ELM-GWO) model to predict compressive strength of concrete with partial replacements for cement", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01081-0.
  125. Shariati, M., Mafipour, M.S., Mehrabi, P., Ahmadi, M., Wakil, K., Trung, N.T. and Toghroli, A. (2020h), "Prediction of concrete strength in presence of furnace slag and fly ash using Hybrid ANN-GA (Artificial Neural Network-Genetic Algorithm)", Smart Struct. Syst., 25(2), 183-195. https://doi.org/10.12989/sss.2020.25.2.183.
  126. Shariati, M., Naghipour, M., Yousofizinsaz, G., Toghroli, A. and Tabarestani, N.P. (2020i), "Numerical study on the axial compressive behavior of built-up CFT columns considering different welding lines", Steel Compos. Struct., 34(3), 377-391 http://doi.org/10.12989/scs.2020.34.3.377.
  127. Shariati, M., Shariati, A., Trung, N.T., Shoaei, P., Ameri, F., Bahrami, N. and Zamanabadi, S.N. (2021b), "Alkali-activated slag (AAS) paste: Correlation between durability and microstructural characteristics", Constr. Build. Mater., 267, 120886. https://doi.org/10.1016/j.conbuildmat.2020.120886.
  128. Shariati, M., Sulong, N.R. and Khanouki, M.A. (2012), "Experimental assessment of channel shear connectors under monotonic and fully reversed cyclic loading in high strength concrete", Mater. Des., 34, 325-331. https://doi.org/10.1016/j.matdes.2011.08.008.
  129. Shariati, M., Sulong, N.R., Shariati, A. and Khanouki, M.A. (2016a), "Behavior of V-shaped angle shear connectors: experimental and parametric study", Mater. Struct., 49(9), 3909-3926. https://doi.org/10.1617/s11527-015-0762-8.
  130. Shariati, M., Sulong, N.R., Shariati, A. and Kueh, A. (2016b), "Comparative performance of channel and angle shear connectors in high strength concrete composites: An experimental study", Constr. Build. Mater., 120, 382-392. https://doi.org/10.1016/j.conbuildmat.2016.05.102.
  131. Shariati, M., Tahmasbi, F., Mehrabi, P., Bahadori, A. and Toghroli, A. (2020j), "Monotonic behavior of C and L shaped angle shear connectors within steel-concrete composite beams: An experimental investigation", Steel Compos. Struct., 35(2), 237-247. http://doi.org/10.12989/scs.2020.35.2.237.
  132. Shokrgozar, A., Safarpour, H. and Habibi, M. (2020), "Influence of system parameters on buckling and frequency analysis of a spinning cantilever cylindrical 3D shell coupled with piezoelectric actuator", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(2), 512-529. https://doi.org/10.1177/0954406219883312.
  133. Soni, S.K., Thomas, B. and Kar, V.R. (2020), "A comprehensive review on CNTs and CNT-reinforced composites: syntheses, characteristics and applications", Mater. Today Commun., 101546.
  134. Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl. Phys., 94(11), 7281-7287 http://doi.org/10.1063/1.1625437.
  135. Taati, E., Borjalilou, V., Fallah, a., Famida and Ahmadian, M.T. (2020), "On size-dependent nonlinear free vibration of carbon nanotube-reinforced beams based on the nonlocal elasticity theory: Perturbation technique", Mech. Based Des. Struct.,
  136. Van Vinh, P. and Tounsi, A. (2021), "The role of spatial variation of the nonlocal parameter on the free vibration of functionally graded sandwich nanoplates", Eng. Comput., 1-19. https://doi.org/10.1007/s00366-021-01475-8.
  137. Vatanpour, V., Jouyandeh, M., Akhi, H., Mousavi Khadem, S.S., Ganjali, M.R., Moradi, H., Mirsadeghi, S., Badiei, A., Esmaeili, A., Rabiee, N., Habibzadeh, S., Koyuncu, I., Nouranian, S., Formela, K. and Saeb, M.R. (2022a), "Hyperbranched polyethylenimine functionalized silica/polysulfone nanocomposite membranes for water purification", Chemosphere, 290, 133363. https://doi.org/10.1016/j.chemosphere.2021.133363.
  138. Vatanpour, V., Jouyandeh, M., Mousavi Khadem, S.S., Paziresh, S., Dehqan, A., Ganjali, M.R., Moradi, H., Mirsadeghi, S., Badiei, A., Munir, M.T., Mohaddespour, A., Rabiee, N., Habibzadeh, S., Mashhadzadeh, A.H., Nouranian, S., Formela, K. and Saeb, M.R. (2022b), "Highly antifouling polymer-nanoparticle-nanoparticle/polymer hybrid membranes", Sci. Total Environ., 810, 152228. https://doi.org/10.1016/j.scitotenv.2021.152228.
  139. Wang, H., Habibi, M., Marzouki, R., Majdi, A., Shariati, M., Denic, N., Zakic, A., Khorami, M., Khadimallah, M.A. and Ebid, A.A.K. (2022a), "Improving the self-healing of cementitious materials with a hydrogel system", Gels, 8(5), 278. https://doi.org/10.3390/gels8050278.
  140. Wang, P., Gao, Z., Pan, F., Moradi, Z., Mahmoudi, T. and Khadimallah, M.A. (2022b), "A couple of GDQM and iteration techniques for the linear and nonlinear buckling of bi-directional functionally graded nanotubes based on the nonlocal strain gradient theory and high-order beam theory", Eng. Anal. Bound. Elem., 143, 124-136. https://doi.org/10.1016/j.enganabound.2022.06.007.
  141. Wang, Q., Zhou, G.Y. and Lin, K.C. (2006), "Scale effect on wave propagation of double-walled carbon nanotubes", Int. J. Solid Struct., 43(20), 6071-6084. https://doi.org/10.1016/j.ijsolstr.2005.11.005
  142. Wang, Y., Yang, J., Moradi, Z., Safa, M. and Khadimallah, M.A. (2022c), "Nonlinear dynamic analysis of thermally deformed beams subjected to uniform loading resting on nonlinear viscoelastic foundation", Eur. J. Mech. A Solids, 95, 104638. https://doi.org/10.1016/j.euromechsol.2022.104638.
  143. Wang, Z., Yu, S., Xiao, Z. and Habibi, M. (2020), "Frequency and buckling responses of a high-speed rotating fiber metal laminated cantilevered microdisk", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2020.1824284.
  144. Wu, J. and Habibi, M. (2021), "Dynamic simulation of the ultra-fast-rotating sandwich cantilever disk via finite element and semi-numerical methods", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-021-01396-6.
  145. Xia, W., Du, J., Habibi, M., Shariati, M. and Khadimallah, M.A. (2022), "Application of Chebyshev-based GDQ and Newmark methods to viscothermoelasticity responses of FG composite annular systems", Eng. Anal. Bound. Elem., 143, 28-42. https://doi.org/10.1016/j.enganabound.2022.06.003.
  146. Xiong, Q.M., Chen, Z., Huang, J.T., Zhang, M., Song, H., Hou, X.F., Li, X.B. and Feng, Z.J. (2020), "Preparation, structure and mechanical properties of Sialon ceramics by transition metal-catalyzed nitriding reaction", Rare Metals, 39(5), 589-596. https://doi.org/10.1007/s12598-020-01385-6
  147. Xu, W., Pan, G., Moradi, Z. and Shafiei, N. (2021), "Nonlinear forced vibration analysis of functionally graded non-uniform cylindrical microbeams applying the semi-analytical solution", Compos. Struct., 114395. https://doi.org/10.1016/j.compstruct.2021.114395.
  148. Yang, N., Moradi, Z., Arvin, H., Muhsen, S. and Khadimallah, M.A. (2022a), "A study on small scale thermal dynamic instability of rotating GPL-reinforced microbeams under principal parametric resonance stimulation of axial and transversal modes regarding the proportional damping", Thin Wall. Struct., 180, 109806. https://doi.org/10.1016/j.tws.2022.109806.
  149. Yang, N., Moradi, Z., Khadimallah, M.A. and Arvin, H. (2022b), "Application of the Chebyshev-Ritz route in determination of the dynamic instability region boundary for rotating nanocomposite beams reinforced with graphene platelet subjected to a temperature increment", Eng. Anal. Bound. Elem., 139, 169-179. https://doi.org/10.1016/j.enganabound.2022.03.013.
  150. Yu, M.F., Files, B.S., Arepalli, S. and Ruoff, R.S. (2000), "Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties", Phys. Rev. Lett., 84(24), 5552-5555 https://doi.org/10.1103/PhysRevLett.84.5552.
  151. Yu, X., Maalla, A. and Moradi, Z. (2022), "Electroelastic high-order computational continuum strategy for critical voltage and frequency of piezoelectric NEMS via modified multi-physical couple stress theory", Mech. Syst. Signal Proc., 165, 108373. https://doi.org/10.1016/j.ymssp.2021.108373.
  152. Zare, R., Najaafi, N., Habibi, M., Ebrahimi, F. and Safarpour, H. (2020), "Influence of imperfection on the smart control frequency characteristics of a cylindrical sensor-actuator GPLRC cylindrical shell using a proportional-derivative smart controller", Smart Struct. Syst., 26(4), 469-480. https://doi.org/10.12989/sss.2020.26.4.469.
  153. Zenkour, A.M. and Abouelregal, A.E. (2015), "Thermoelastic interaction in functionally graded nanobeams subjected to time-dependent heat flux", Steel Compos. Struct., 18(4), 909-924. https://doi.org/10.12989/scs.2015.18.4.909.
  154. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. https://doi.org/10.12989/sem.2021.78.2.117.
  155. Zhang, Y., Wang, Z., Tazeddinova, D., Ebrahimi, F., Habibi, M. and Safarpour, H. (2021), "Enhancing active vibration control performances in a smart rotary sandwich thick nanostructure conveying viscous fluid flow by a PD controller", Wave Random Complex Med., 1-24. https://doi.org/10.1080/17455030.2021.1948627.
  156. Zhang, Y.Q., Liu, G.R. and Xie, X.Y. (2005), "Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity", Phys. Rev. B, 71(19), 1-7. https://doi.org/10.1103/PhysRevB.71.195404.
  157. Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. "Bending and stress responses of the hybrid axisymmetric system via state-space method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.
  158. Zheng, W., Liu, J., Oyarhossein, M.A., Safarpour, H. and Habibi, M. (2023), "Prediction of nth-order derivatives for vibration responses of a sandwich shell composed of a magnetorheological core and composite face layers", Eng. Anal. Bound. Elem., 146, 170-183. https://doi.org/10.1016/j.enganabound.2022.10.019.
  159. Zheng, Y., Jin, H., Jiang, C., Moradi, Z., Khadimallah, M.A. and Moayedi, H. (2022), "Analyzing behavior of circular concrete-filled steel tube column using improved fuzzy models", Steel Compos. Struct., 43(5), 625-637. https://doi.org/10.12989/scs.2022.43.5.625.
  160. Zhou, C., Zhao, Y., Zhang, J., Fang, Y. and Habibi, M. (2020), "Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system", Adv. Nano Res., 9(4), 295-307. https://doi.org/10.12989/anr.2020.9.4.295.
  161. Zhu, L., Ren, H., Habibi, M., Mohammed, K.J. and Khadimallah, M.A. (2022), "Predicting the environmental economic dispatch problem for reducing waste nonrenewable materials via an innovative constraint multi-objective Chimp Optimization Algorithm", J. Clean. Prod., 132697. https://doi.org/10.1016/j.jclepro.2022.132697.
  162. Zhu, X. and Li, L. (2017), "Longitudinal and torsional vibrations of size-dependent rods via nonlocal integral elasticity", Int. J. Mech. Sci., 133, 639-650. https://doi.org/10.1016/j.ijmecsci.2017.09.030.