Advances in nano research

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Vibrational characteristics of multi-phase nanocomposite reinforced circular/annular system

  • Zhou, Changlin (School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology) ;
  • Zhao, Yi (China Construction Third Engineering Co., Ltd,) ;
  • Zhang, Ji (School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology) ;
  • Fang, Yuan (China Construction Third Engineering Co., Ltd,) ;
  • Habibi, Mostafa (Institute of Research and Development, Duy Tan University)
  • Received : 2020.08.17
  • Accepted : 2020.10.17
  • Published : 2020.11.25
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Abstract

The vibrational characteristics of Multi-Phase Nanocomposite (MPC) reinforced annular/circular plate under initially stresses are presented using the state-space formulation based on three-dimensional elasticity theory (3D-elasticity theory) and Differential Quadrature Method (DQM). The MPC reinforced annular/circular plate is under initial lateral stress and composed of multilayers with Carbon Nanotubes (CNTs) uniformly dispersed in each layer, but its properties change layer-by-layer along the thickness direction. The State-Space based Differential Quadrature Method (SS-DQM) is presented to examine the frequency behavior of the current structure. Halpin-Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. A singular point is investigated for modeling the circular plate. The CNTs are supposed to be randomly oriented and uniformly distributed through the matrix of epoxy resin. Afterward, a parametric study is done to present the effects of various types of sandwich circular/annular plates on frequency characteristics of the MPC reinforced annular/circular plate using 3D-elasticity theory.

Keywords

Acknowledgement

Financial support by the National Natural Science Foundation of China (NSFC) (Grant Nos. 51378377, 41872001), Fundamental Research Funds for the Central Universities (Grant No. 2016YXMS094), and China Construction Third Engineering Bureau Group Co., Ltd (grant No. CSCEC3Z-2019-03) is much appreciated.

References

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, Int. J., 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  2. Aghajani, G. and Ghadimi, N. (2018), "Multi-objective energy management in a micro-grid", Energy Rep., 4, 218-225. https://doi.org/10.1016/j.egyr.2017.10.002.
  3. Akbary, P., Ghiasi, M., Pourkheranjani, M.R.R., Alipour, H. and Ghadimi, N. (2019), "Extracting appropriate nodal marginal prices for all types of committed reserve", Comput. Econ., 53(1), 1-26. https://doi.org/10.1007/s10614-017-9716-2.
  4. Al-Furjan, M., Alzahrani, B., Shan, L., Habibi, M. and Jung, D.W. (2020a), "Nonlinear forced vibrations of nanocomposite-reinforced viscoelastic thick annular system under hygrothermal environment", Mech. Based Des. Struct. Mach., 2020, 1-27. https://doi.org/10.1080/15397734.2020.1824795.
  5. Al-Furjan, M., Bolandi, S.Y., Shan, L., Habibi, M. and Jung, D.W. (2020b), "On the vibrations of a high-speed rotating multi-hybrid nanocomposite reinforced cantilevered microdisk", Mech. Based Des. Struct. Mach., 2020, 1-29. https://doi.org/10.1080/15397734.2020.1828098.
  6. Al-Furjan, M., Fereidouni, M., Habibi, M., Abd Ali, R., Ni, J. and Safarpour, M. (2020c), "Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework", Eng. Comput., 2020, 1-23. https://doi.org/10.1007/s00366-020-01177-7.
  7. Al-Furjan, M., Habibi, M. and Safarpour, H. (2020d), "Vibration control of a smart shell reinforced by graphene nanoplatelets", Int. J. Appl. Mech., 12(6), 2050066. https://doi.org/10.1142/S1758825120500660.
  8. Al-Furjan, M., Habibi, M., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020e), "Chaotic oscillation of a multi-scale hybrid nano-composites reinforced disk under harmonic excitation via GDQM", Compos. Struct., 252, 112737. https://doi.org/10.1016/j.compstruct.2020.112737.
  9. Al-Furjan, M., Habibi, M., Chen, G., Safarpour, H., Safarpour, M. and Tounsi, A. (2020f), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 2020, 1-24. https://doi.org/10.1007/s00366-020-01144-2.
  10. Al-Furjan, M., 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., 2020, 1-18. https://doi.org/10.1007/s00366-020-01130-8.
  11. Al-Furjan, M., Habibi, M., Jung, D.W., Chen, G., Safarpour, M. and Safarpour, H. (2020h), "Chaotic responses and nonlinear dynamics of the graphene nanoplatelets reinforced doubly-curved panel", Eur. J. Mech. A Solids, 85, 104091. https://doi.org/10.1016/j.euromechsol.2020.104091.
  12. Al-Furjan, M., Mohammadgholiha, M., Alarifi, I.M., Habibi, M. and Safarpour, H. (2020i), "On the phase velocity simulation of the multi curved viscoelastic system via an exact solution framework", Eng. Comput., 2020, 1-17. https://doi.org/10.1007/s00366-020-01152-2.
  13. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H. and Jung, D.W. (2020j), "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.
  14. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H. and Jung, D.W. (2020k), "Wave propagation simulation in an electrically open shell reinforced with multi-phase nanocomposites", Eng. Comput., 2020, 1-17. https://doi.org/10.1007/s00366-020-01167-9.
  15. Al-Furjan, M., Oyarhossein, M.A., Habibi, M., Safarpour, H., Jung, D.W. and Tounsi, A. (2020l), "On the wave propagation of the multi-scale hybrid nanocomposite doubly curved viscoelastic panel", Compos. Struct., 255, 112947. https://doi.org/10.1016/j.compstruct.2020.112947
  16. Al-Furjan, M., Safarpour, H., Habibi, M., Safarpour, M. and Tounsi, A. (2020m), "A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method", Eng. Comput., 2020, 1-18. https://doi.org/10.1007/s00366-020-01088-7.
  17. Alibeigloo, A. (2017), "Three dimensional coupled thermoelasticity solution of sandwich plate with FGM core under thermal shock", Compos. Struct., 177, 96-103. https://doi.org/10.1016/j.compstruct.2017.06.046.
  18. Alibeigloo, A. (2020), "Three-dimensional thermoelasticity analysis of graphene platelets reinforced cylindrical panel", Eur. J. Mech. A Solids, 81, 103941. https://doi.org/10.1016/j.euromechsol.2019.103941.
  19. Alibeigloo, A. and Noee, A.R.P. (2017), "Static and free vibration analysis of sandwich cylindrical shell based on theory of elasticity and using DQM", Acta Mechanica, 228(12), 4123-4140. https://doi.org/10.1007/s00707-017-1914-4.
  20. 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., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  21. Allam, O., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Mahmoud, S., Adda Bedia, E. and Tounsi, A. (2020), "A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells", Comput. Concrete, Int. J., 26(2), 185-201. http://dx.doi.org/10.12989/cac.2020.26.2.185.
  22. Ansari, R., Torabi, J. and Shojaei, M.F. (2017), "Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading", Compos. Part B Eng., 109, 197-213. https://doi.org/10.1016/j.compositesb.2016.10.050.
  23. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin-Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007.
  24. Azimi, S. (1988), "Free vibration of circular plates with elastic edge supports using the receptance method", J. Sound Vib., 120(1), 19-35. https://doi.org/10.1016/0022-460X(88)90332-X.
  25. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, Int. J., 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  26. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., Int. J., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.
  27. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A. and Mahmoud, S. (2020), "Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory", Smart Struct. Syst., Int. J., 25(4), 409-422. https://doi.org/10.12989/sss.2020.25.4.409.
  28. 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., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  29. Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, Int. J., 25(6), 485-495. https://doi.org/10.12989/cac.2020.25.6.485
  30. Bousahla, A.A., Bourada, F., Mahmoud, S., Tounsi, A., Algarni, A., Bedia, E. and Tounsi, A. (2020), "Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory", Comput. Concrete, Int. J., 25(2), 155-166. https://doi.org/10.12989/cac.2020.25.2.155.
  31. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., Int. J., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  32. 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., Int. J., 7(3), 191-208. https://doi.org/10.12989/anr.2019.7.3.191.
  33. Chakrapani, S.K., Barnard, D.J. and Dayal, V. (2016), "Nonlinear forced vibration of carbon fiber/epoxy prepreg composite beams: Theory and experiment", Compos. Part B Eng., 91, 513-521. https://doi.org/10.1016/j.compositesb.2016.02.009.
  34. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., Int. J., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  35. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., Int. J., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  36. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369.
  37. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019). "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  38. Ebrahimi, F. and Jafari, A. (2017), "Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory", Adv. Nano Res., Int. J., 5(4), 281-301. https://doi.org/10.12989/anr.2017.5.4.281.
  39. Ebrahimi, F. and Salari, E. (2019), "Effect of non-uniform temperature distributions on nonlocal vibration and buckling of inhomogeneous size-dependent beams", Adv. Nano Res., Int. J., 6(4), 377-397. https://doi.org/10.12989/anr.2018.6.4.377.
  40. Ebrahimi, F., Karimiasl, M., Civalek, O. and Vinyas, M. (2019), "Surface effects on scale-dependent vibration behavior of flexoelectric sandwich nanobeams", Adv. Nano Res., Int. J., 7(2), 77-88. https://doi.org/10.12989/anr.2019.7.2.077.
  41. Ebrahimi, F., Jafari, A. and Selvamani, R. (2020a), "Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment", Adv. Nano Res., Int. J., 8(1), 83-94. https://doi.org/10.12989/anr.2020.8.1.083.
  42. 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.
  43. Ehyaei, J. and Daman, M. (2017), "Free vibration analysis of double walled carbon nanotubes embedded in an elastic medium with initial imperfection", Adv. Nano Res., Int. J., 5(2), 179-192. https://doi.org/10.12989/anr.2017.5.2.179.
  44. Emam, S. and Eltaher, M. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029.
  45. Emdadi, M., Mohammadimehr, M. and Navi, B.R. (2019), "Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method", Adv. Nano Res., Int. J., 7(2), 109. https://doi.org/10.12989/anr.2019.7.2.109.
  46. Eslami, M., Moghadam, H.A., Zayandehroodi, H. and Ghadimi, N. (2019), "A new formulation to reduce the number of variables and constraints to expedite SCUC in bulky power systems", Proc. Nat. Aca. Sci. Ind. Sec. A Phys. Sci., 89(2), 311-321. https://doi.org/10.1007/s40010-017-0475-1.
  47. Firouz, M.H. and Ghadimi, N. (2016), "Concordant controllers based on FACTS and FPSS for solving wide-area in multi-machine power system", J. Intell. Fuzzy Syst., 30(2), 845-859. https://doi.org/10.3233/IFS-151807.
  48. Ghabussi, A., Ashrafi, N., Shavalipour, A., Hosseinpour, A., Habibi, M., Moayedi, H., Babaei, B. and Safarpour, H. (2019), "Free vibration analysis of an electro-elastic GPLRC cylindrical shell surrounded by viscoelastic foundation using modified length-couple stress parameter", Mech. Based Des. Struct. Mach., 2020, 1-25. https://doi.org/10.1080/15397734.2019.1705166.
  49. Ghabussi, A., Marnani, J.A. and Rohanimanesh, M.S. (2020), "Improving seismic performance of portal frame structures with steel curved dampers", Structures, 24, 27-40. https://doi.org/10.1016/j.istruc.2019.12.025.
  50. Ghannadpour, S. and Moradi, F. (2019), "Nonlocal nonlinear analysis of nano-graphene sheets under compression using semi-Galerkin technique", Adv. Nano Res., Int. J., 7(5), 311-324. https://doi.org/10.12989/anr.2019.7.5.311.
  51. Gheydi, M., Nouri, A. and Ghadimi, N. (2016), "Planning in microgrids with conservation of voltage reduction", IEEE Syst. J., 12(3), 2782-2790. https://doi.org/10.1109/JSYST.2016.2633512.
  52. Gollou, A.R. and Ghadimi, N. (2017), "A new feature selection and hybrid forecast engine for day-ahead price forecasting of electricity markets", J. Intell. Fuzzy Syst., 32(6), 4031-4045. https://doi.org/10.3233/JIFS-152073.
  53. Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct. Mach., 2019, 1-19. https://doi.org/10.1080/15397734.2019.1697932.
  54. 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. Mach., 2020, 1-22. https://doi.org/10.1080/15397734.2020.1779086.
  55. Hamian, M., Darvishan, A., Hosseinzadeh, M., Lariche, M.J., Ghadimi, N. and Nouri, A. (2018), "A framework to expedite joint energy-reserve payment cost minimization using a custom-designed method based on mixed integer genetic algorithm", Eng. Appl. Artif. Intell., 72, 203-212. https://doi.org/10.1016/j.engappai.2018.03.022.
  56. Hosseini Firouz, M. and Ghadimi, N. (2016), "Optimal preventive maintenance policy for electric power distribution systems based on the fuzzy AHP methods", Complexity, 21(6), 70-88. https://doi.org/10.1002/cplx.21668.
  57. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis", Comput. Concrete, Int. J., 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  58. Karimiasl, M., Ebrahimi, F. and Akgoz, B. (2019), "Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading", Compos. Struct., 223, 110988. https://doi.org/10.1016/j.compstruct.2019.110988.
  59. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S. (2020), "Analytical modeling of bending and vibration of thick advanced composite plates using a fourvariable quasi 3D HSDT", Eng. Comput., 36(3), 807-821. https://doi.org/10.1007/s00366-019-00732-1.
  60. Khodaei, H., Hajiali, M., Darvishan, A., Sepehr, M. and Ghadimi, N. (2018), "Fuzzy-based heat and power hub models for costemission operation of an industrial consumer using compromise programming", Appl. Therm. Eng., 137, 395-405. https://doi.org/10.1016/j.applthermaleng.2018.04.008.
  61. Kim, M., Park, Y.B., Okoli, O.I. and Zhang, C. (2009), "Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites", Compos. Sci. Technol., 69(3-4), 335-342. https://doi.org/10.1016/j.compscitech.2008.10.019.
  62. Leng, H., Li, X., Zhu, J., Tang, H., Zhang, Z. and Ghadimi, N. (2018), "A new wind power prediction method based on ridgelet transforms, hybrid feature selection and closed-loop forecasting", Adv. Eng. Inf., 36, 20-30. https://doi.org/10.1016/j.aei.2018.02.006.
  63. Liu, Y., Wang, W. and Ghadimi, N. (2017), "Electricity load forecasting by an improved forecast engine for building level consumers", Energy, 139, 18-30. https://doi.org/10.1016/j.energy.2017.07.150.
  64. 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., 2020, 1-20. https://doi.org/10.1007/s00366-020-01004-z.
  65. Maghamikia, S. and Jam, J. (2011), "Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM", J. Mech. Sci. Technol., 25(11), 2805-2810. https://10.1007/s12206-011-0738-8.
  66. 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., Int. J., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  67. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Adda Bedia, E. and Mahmoud, S. (2020), "A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions", Steel Compos. Struct., Int. J., 36(3), 355-367. https://doi.org/10.12989/scs.2020.36.3.355.
  68. Mirzapour, F., Lakzaei, M., Varamini, G., Teimourian, M. and Ghadimi, N. (2019), "A new prediction model of battery and wind-solar output in hybrid power system", J. Amb. Intell. Human. Comput., 10(1), 77-87. https://doi.org/10.1007/s12652-017-0600-7.
  69. 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.
  70. Moayedi, H., Darabi, R., Ghabussi, A., Habibi, M. and Foong, L.K. (2020b), "Weld orientation effects on the formability of tailor welded thin steel sheets", Thin-Wall. Struct., 149, 106669. https://doi.org/10.1016/j.tws.2020.106669.
  71. 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.
  72. Parand, A.A. and Alibeigloo, A. (2017), "Static and vibration analysis of sandwich cylindrical shell with functionally graded core and viscoelastic interface using DQM", Compos. Part B Eng., 126, 1-16. https://doi.org/10.1016/j.compositesb.2017.05.071.
  73. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S. and Tounsi, A. (2020), "A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Geomech. Eng., Int. J., 22(2), 119-132. https://doi.org/10.12989/gae.2020.22.2.119.
  74. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96, 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005.
  75. Rafiee, M., Liu, X., He, X. and Kitipornchai, S. (2014), "Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates", J. Sound Vib., 333(14), 3236-3251. https://doi.org/10.1016/j.jsv.2014.02.033.
  76. Rahimi, A., Alibeigloo, A. and Safarpour, M. (2020), "Three-dimensional static and free vibration analysis of graphene platelet-reinforced porous composite cylindrical shell", J. Vib. Control, 1077546320902340. https://doi.org/10.1177/1077546320902340.
  77. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a fourunknown refined integral plate theory", Comput. Concrete., Int. J., 25(3), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  78. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E., Mahmoud, S., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete., Int. J., 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  79. Safarpour, M., Rahimi, A. and Alibeigloo, A. (2019a), "Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM", Mech. Based Des. Struct. Mach., 2019, 1-29. https://doi.org/10.1080/15397734.2019.1646137
  80. Safarpour, M., Rahimi, A., Alibeigloo, A., Bisheh, H. and Forooghi, A. (2019b), "Parametric study of three-dimensional bending and frequency of FG-GPLRC porous circular and annular plates on different boundary conditions", Mech. Based Des. Struct. Mach., 2019, 1-31. https://doi.org/10.1080/15397734.2019.1701491.
  81. Safarpour, M., Ghabussi, A., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "Frequency characteristics of FG-GPLRC viscoelastic thick annular plate with the aid of GDQM", Thin-Wall. Struct., 150, 106683. https://doi.org/10.1016/j.tws.2020.106683.
  82. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., Int. J., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  83. Salari, F.E.E. (2016), "Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams", Adv. Nano Res., Int. J., 4(3), 197-228. https://doi.org/10.12989/anr.2016.4.3.197.
  84. Salehipour, H., Shahgholian-Ghahfarokhi, D., Shahsavar, A., Civalek, O. and Edalati, M. (2020), "Static deflection and free vibration analysis of functionally graded and porous cylindrical micro/nano shells based on the three-dimensional elasticity and modified couple stress theories", Mech. Based Des. Struct. Mach., 2020, 1-22. https://doi.org/10.1080/15397734.2020.1775095.
  85. Shaban, M. and Alibeigloo, A. (2020), "Global bending analysis of corrugated sandwich panels with integrated piezoelectric layers", J. Sandw. Struct. Mater., 22(4), 1055-1073. https://doi.org/10.1177/1099636218780172.
  86. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated composite plates", Adv. Nano Res., Int. J., 7(5), 337-349. https://doi.org/10.12989/anr.2019.7.5.337.
  87. Shen, H.S. (2009), "A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators", Compos. Struct., 91(3), 375-384. https://doi.org/10.1016/j.compstruct.2009.06.005.
  88. Shokrgozar, A., Ghabussi, A., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "Viscoelastic dynamics and static responses of a graphene nanoplatelets-reinforced composite cylindrical microshell", Mech. Based Des. Struct. Mach., 2020, 1-28. https://doi.org/10.1080/15397734.2020.1719509.
  89. Shu, C. (2012), Differential Quadrature and Its Application in Engineering, Springer Science & Business Media, London, UK.
  90. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations", Int. J. Num. Methods Fluids, 15(7), 791-798. https://doi.org/10.1002/fld.1650150704.
  91. Tahouneh, V. and Eskandari-Jam, J. (2014), "A semi-analytical solution for 3-D dynamic analysis of thick continuously graded carbon nanotube-reinforced annular plates resting on a Two-parameter elastic foundation", Mech. Adv. Compos. Struct., 1(2), 113-130. https://doi.org/10.22075/macs.2014.286.
  92. Tahouneh, V. and Yas, M. (2014), "Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates", Polym. Compos., 35(8), 1644-1661. https://doi.org/10.1002/pc.22818.
  93. Thostenson, E., Li, W., Wang, D., Ren, Z. and Chou, T. (2002), "Carbon nanotube/carbon fiber hybrid multiscale composites", J. Appl. Phys., 91(9), 6034-6037. https://doi.org/10.1063/1.1466880.
  94. Tounsi, A., Benguediab, S., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001.
  95. Tounsi, A., Al-Dulaijan, S., Al-Osta, M.A., Chikh, A., Al-Zahrani, M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., Int. J., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  96. Van Do, V.N. and Lee, C.H. (2020), "Static bending and free vibration analysis of multilayered composite cylindrical and spherical panels reinforced with graphene platelets by using isogeometric analysis method", Eng. Struct., 215, 110682. https://doi.org/10.1016/j.engstruct.2020.110682.
  97. Wang, Q., Quek, S., Sun, C. and Liu, X. (2001), "Analysis of piezoelectric coupled circular plate", Smart Mater. Struct., 10(2), 229. https://doi.org/10.1088/0964-1726/10/2/308/meta
  98. Wu, T., Wang, Y. and Liu, G. (2002), "Free vibration analysis of circular plates using generalized differential quadrature rule", Comput. Methods Appl. Mech. Eng., 191(46), 5365-5380. https://doi.org/10.1016/S0045-7825(02)00463-2.
  99. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams", Appl. Math. Model., 42, 735-752. https://doi.org/10.1016/j.apm.2016.10.045.
  100. Wu, C.P., Chen, Y.H., Hong, Z.L. and Lin, C.H. (2018), "Nonlinear vibration analysis of an embedded multi-walled carbon nanotube", Adv. Nano Res., Int. J., 6(2), 163-182. https://doi.org/10.12989/anr.2018.6.2.163.
  101. Yu, D. and Ghadimi, N. (2019), "Reliability constraint stochastic UC by considering the correlation of random variables with Copula theory", IET Renew. Pow. Gen., 13(14), 2587-2593. https://doi.org/10.1049/iet-rpg.2019.0485.
  102. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Adda Bedia, E., Mahmoud, S. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, Int. J., 26(1), 63-74. http://dx.doi.org/10.12989/cac.2020.26.1.063.