Steel and Composite Structures

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Poroelastic vibrations of FG Porous higher-order shear deformable

  • Jing Li (School of Intelligent Construction, Wuchang University of Technology) ;
  • Fei Tang (School of Intelligent Construction, Wuchang University of Technology) ;
  • Yasser Alashker (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Farhan Alhosny (Mechanical Engineering Department, UAE University)
  • Received : 2023.03.11
  • Accepted : 2023.10.12
  • Published : 2023.12.10
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Abstract

In the current examination, a trigonometric shear deformation theory is hired to govern natural frequencies of a functionally graded porous microplate which is covered by two nanocomposite layers. The properties of the structure are varied based on the specified patterns. Utilizing the modified form of couple stress theory for taking the scale effect into account in conjunction with Hamilton's principle, the motion equations are obtained. Then, they are solved via Fourier series functions as an analytical approach. After confirming the results' accuracy, various parameters' effect on the results is investigated. Designing and manufacturing more efficient structures, especially those that are subjected to multi-physical loads can be accounted as findings of this work.

Keywords

Acknowledgement

The third author extends his appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through the large Research Group Program Under Grant number RGP2/180/44.

References

  1. AkhavanAlavi, S.M., Mohammadimehr, M. and Edjtahed, S.H. (2019), "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Europ. J. Mech., A/Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  2. Aktas, C., Polat, O., Beitollahpoor, M., Farzam, M., Pesika, N.S. and Sahiner, N. (2023), "Force-based characterization of the wetting properties of LDPE surfaces treated with CF4 and H2 plasmas", Polymers, 15(9), 2132. https://doi.org/10.3390/polym15092132.
  3. Al-Furjan, M.S.H., Habibi, M., Jung, D. won, Sadeghi, S., Safarpour, H., Tounsi, A. and Chen, G. (2020), "A computational framework for propagated waves in a sandwich doubly curved nanocomposite panel", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01130-8.
  4. Alhaifi, K., Arshid, E. and Khorshidvand, A.R. (2021), "Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM", Steel Compos. Struct., 39(6), 795-809. https://doi.org/10.12989/scs.2021.39.6.795.
  5. Alhaifi, K., Khorshidvand, A.R., Al-Masoudy, M.M., Arshid, E. and Madani, S.H. (2023), "A shooting method for buckling and post-buckling analyses of FGSP circular plates considering various patterns of Pores' placement", Struct. Eng. Mech., 85(3), 419-432. https://doi.org/10.12989/sem.2023.85.3.419.
  6. Alibeigloo, A. (2013), "Static analysis of functionally graded carbon nanotube-reinforced composite plate embedded in piezoelectric layers by using theory of elasticity", Compos. Struct., 95, 612-622. https://doi.org/10.1016/j.compstruct.2012.08.018
  7. Allahkarami, F. and Nikkhah-Bahrami, M. (2018), "The effects of agglomerated CNTs as reinforcement on the size-dependent vibration of embedded curved microbeams based on modified couple stress theory", Mech. Adv. Mater. Struct., 25(12), 995-1008. https://doi.org/10.1080/15376494.2017.1323144.
  8. Amir, S., Arshid, E. and Ghorbanpour Arani, M.R. (2019), "Size-dependent magneto-electro-elastic vibration analysis of FG saturated porous annular/ circular micro sandwich plates embedded with nano-composite face sheets subjected to multi-physical pre loads", Smart Struct. Syst., 23(5), 429-447. https://doi.org/10.12989/sss.2019.23.5.429.
  9. Amir, S., Arshid, E. and Maraghi, Z.K. (2020), "Free vibration analysis of magneto-rheological smart annular three-layered plates subjected to magnetic field in viscoelastic medium", Smart Struct. Syst., 25(5), 581-592. https://doi.org/10.12989/sss.2020.25.5.581.
  10. Amir, S., Arshid, E., Rasti-Alhosseini, S.M.A. and Loghman, A. (2020), "Quasi-3D tangential shear deformation theory for size-dependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environment", J. Thermal Stresses, 43(2), 133-156. https://doi.org/10.1080/01495739.2019.1660601.
  11. Amir, S., Bidgoli, E.M.R. and Arshid, E. (2020), "Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT", Mech. Adv. Mater. Struct., 27(8), 605-619. https://doi.org/10.1080/15376494.2018.1487612.
  12. Amir, S., Khani, M., Shajari, A.R. and Dashti, P. (2017), "Instability analysis of viscoelastic CNTs surrounded by a thermo-elastic foundation", Struct. Eng. Mech., 63(2), 171-180. https://doi.org/10.12989/sem.2017.63.2.171.
  13. Amir, S., Khorasani, M. and BabaAkbar-Zarei, H. (2018), "Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory", J. Sandw. Struct. Mater., 109963621879538. https://doi.org/10.1177/1099636218795385.
  14. Anh, V.T.T., Huong, V.T., Nguyen, P.D. and Duc, N.D. (2021), "Nonlinear dnamic analysis of porous graphene platelet-reinforced composite sandwich shallow spherical shells", Mech. Compos. Mater., 57(5), 609-622. https://doi.org/10.1007/S11029-021-09983-W/METRICS.
  15. Ansari, R., Shahabodini, A., Alipour, A. and Rouhi, H. (2012), "Stability of a single-layer graphene sheet with various edge conditions: A non-local plate model including interatomic potentials", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 226(2), 51-60. https://doi.org/10.1177/1740349912451209.
  16. Ansari, R., Torabi, J. and Hosein Shakouri, A. (2017), "Vibration analysis of functionally graded carbon nanotube-reinforced composite elliptical plates using a numerical strategy", Aeros. Sci. Technol., 60, 152-161. https://doi.org/10.1016/j.ast.2016.11.004.
  17. Anumandla, V. and Gibson, R.F. (2006), "A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites", Compos. Part A: Appl. Sci. Manufact., 37(12), 2178-2185. https://doi.org/10.1016/j.compositesa.2005.09.016.
  18. Arani, A.G. and Abdollahian, M. (2017), "Transient response of FG higher-order nanobeams integrated with magnetostrictive layers using modified couple stress theory", Mech. Adva. Mater. Struct., 1-13. https://doi.org/10.1080/15376494.2017.1387326.
  19. Arani, A.G., Jafari, G.S. and Kolahchi, R. (2018), "Vibration analysis of nanocomposite microplates integrated with sensor and actuator layers using surface SSDPT", Polymer Compos., 39(6), 1936-1949. https://doi.org/10.1002/pc.24150.
  20. Arshid, E., Amir, S. and Loghman, A., (2020), "Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT", Int. J. Mech. Sci., 180(March), 105656. https://doi.org/10.1016/j.ijmecsci.2020.105656.
  21. Arshid, E., Amir, S. and Loghman, A., (2021a), "Thermal buckling analysis of FG graphene nanoplatelets reinforced porous nanocomposite MCST-based annular/circular microplates", Aeros. Sci. Technol., 111, 106561. https://doi.org/10.1016/j.ast.2021.106561.
  22. Arshid, E., Amir, S. and Loghman, A., (2021b), "Bending and buckling behaviors of heterogeneous temperature-dependent micro annular/circular porous sandwich plates integrated by FGPEM nano-Composite layers", J. Sandw. Struct. Mater., 23(8), 3836-3877. https://doi.org/10.1177/1099636220955027.
  23. Arshid, E., Amir, S. and Loghman, A., (2023a), "Thermoelastic vibration characteristics of asymmetric annular porous reinforced with nano-fillers microplates embedded in an elastic medium: CNTs Vs. GNPs", Archiv. Civil Mech. Eng., 23(2), 100. https://doi.org/10.1007/s43452-023-00624-8.
  24. Arshid, E., Amir, S. and Loghman, A., (2023b), "On the vibrations of FG GNPs-RPN annular plates with piezoelectric/metallic coatings on Kerr elastic substrate considering size dependency and surface stress effects", Acta Mech., 1-42. https://doi.org/10.1007/s00707-023-03593-4.
  25. Arshid, E., Arshid, H., Amir, S. and Mousavi, S.B. (2021), "Free vibration and buckling analyses of FG porous sandwich curved microbeams in thermal environment under magnetic field based on modified couple stress theory", Archives Civil Mech. Eng., 21(1), 6. https://doi.org/10.1007/s43452-020-00150-x.
  26. Arshid, E., Ghorbani, M.A., Momeni Nia, M.J., Civalek, O . and Kumar, A. (2023), "Thermo-elastic buckling behaviors of advanced fluid-infiltrated porous shells integrated with GPLs-reinforced nanocomposite patches", Mech. Adv. Mater. Struct., 1-17. https://doi.org/10.1080/15376494.2023.2251015.
  27. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2022), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput., 38, 4051-4072. https://doi.org/10.1007/s00366-021-01382-y.
  28. 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(January), 220-233. https://doi.org/10.1016/j.tws.2018.01.007.
  29. Arshid, E., Momeni Nia, M.J., Ghorbani, M.A., Civalek, O . and Kumar, A. (2023), "On the poroelastic vibrations of lightweight FGSP doubly-curved shells integrated with GNPs-reinforced composite coatings in thermal atmospheres", Appl. Mathem. Modelling, 124, 122-141. https://doi.org/10.1016/j.apm.2023.07.036.
  30. Arshid, E., Soleimani-Javid, Z., Amir, S. and Duc, N.D. (2022), "Higher-order hygro-magneto-electro-thermomechanical analysis of FG-GNPs-reinforced composite cylindrical shells embedded in PEM layers", Aeros. Sci. Technol., 126, 107573. https://doi.org/10.1016/j.ast.2022.107573.
  31. 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.
  32. Babaei, M., Asemi, K. and Safarpour, P. (2019), "Buckling and static analyses of functionally graded saturated porous thick beam resting on elastic foundation based on higher order beam theory", Iran. J. Mech. Eng. Transact. ISME, 20(1), 94-112.
  33. Babaei, M. and Asemi, K. (2020), "Static, dynamic and natural frequency analyses of functionally graded carbon nanotube annular sector plates resting on viscoelastic foundation", SN Appl. Sci., 2(10), 1652. https://doi.org/10.1007/s42452-020-03421-7.
  34. Balasundaram, G. and Webster, T.J. (2006), "Nanotechnology and biomaterials for orthopedic medical applications", Nanomedicine, 1(2), 169-176. https://doi.org/10.2217/17435889.1.2.169.
  35. Barati, M.R. (2018a), "Nonlocal stress-strain gradient vibration analysis of heterogeneous double-layered plates under hygrothermal and linearly varying in-plane loads", JVC/J. Vib. Control, 24(19), 4630-4647. https://doi.org/10.1177/1077546317731672.
  36. Barati, M.R. (2018b), "Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity", Acta Mech., 229(3), 1183-1196. https://doi.org/10.1007/s00707-017-2032-z.
  37. Behravan Rad, A. and Shariyat, M. (2015), "Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations", Compos. Struct., 125, 558-574. https://doi.org/10.1016/J.COMPSTRUCT.2015.02.049.
  38. Bui, T.Q., Do, T. Van, Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T., Nguyen-Van, T.A., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos. Part B: Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  39. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (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.
  40. Chan, D.Q., Van Thanh, N., Khoa, N.D. and Duc, N.D. (2020), "Nonlinear dynamic analysis of piezoelectric functionally graded porous truncated conical panel in thermal environments", Thin-Wall. Struct., 154, 106837. https://doi.org/10.1016/j.tws.2020.106837.
  41. Chen, D., Yang, J. and Kitipornchai, S. (2019), "Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method", Archiv. Civil Mech. Eng., 19(1), 157-170. https://doi.org/10.1016/J.ACME.2018.09.004.
  42. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aeros. Sci. Technol, 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020.
  43. Damghanian, R., Asemi, K. and Babaei, M., (2022), "A new beam element for static, free and forced vibration responses of microbeams resting on viscoelastic foundation based on modified couple stress and third-order beam theories", Iran. J. Sci. Technol. Transact. Mech. Eng., 46(1), 131-147. https://doi.org/10.1007/s40997-020-00407-z.
  44. Dat, N.D., Quan, T.Q. and Duc, N.D. (2021), "Nonlinear thermal dynamic buckling and global optimization of smart sandwich plate with porous homogeneous core and carbon nanotube reinforced nanocomposite layers", Europ. J. Mech. - A/Solids, 90, 104351. https://doi.org/10.1016/J.EUROMECHSOL.2021.104351.
  45. Dat, N.D., Thanh, N. Van, MinhAnh, V. and Duc, N.D. (2022), "Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer", Mech. Adv. Mater. Struct., 29(10), 1431-1448. https://doi.org/10.1080/15376494.2020.1822476.
  46. Duc, N.D. (2014), "Nonlinear static and dynamic stability of functionally graded plates and shells", Vietnam Nat. Univ. Press.
  47. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P. and Thanh, N. Van, (2017a), "Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations", Thin-Wall. Struct., 115, 300-310. https://doi.org/10.1016/j.tws.2017.02.016.
  48. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P. and Thanh, N. Van, (2017b), "Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations", Thin-Wall. Struct., 115, 300-310. https://doi.org/10.1016/j.tws.2017.02.016.
  49. Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018a), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mech., 4(4), 245-259. https://doi.org/10.22055/jacm.2018.23219.1151.
  50. Duc, N.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018b), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mech., 4(4), 245-259. https://doi.org/10.22055/jacm.2018.23219.1151.
  51. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092.
  52. Ebrahimi, F. and Barati, M.R. (2017b), "Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct., 24(11), 924-936. https://doi.org/10.1080/15376494.2016.1196795.
  53. Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030.
  54. Eringen, A. and Wegner, J. (2003), "Nonlocal continuum field theories", Appl. Mech. Rev., 56(2), B20-B22. https://doi.org/10.1115/1.1553434.
  55. 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.
  56. Esawi, A.M.K. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022.
  57. Faraji Oskouie, M., Ansari, R. and Rouhi, H. (2021), "Investigating vibrations of viscoelastic fluid-conveying carbon nanotubes resting on viscoelastic foundation using a nonlocal fractional Timoshenko beam model", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 235(1-2), 30-40. https://doi.org/10.1177/2397791420931701.
  58. Fattahi, A.M., Safaei, B. and Moaddab, E. (2019), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., 32(2), 281-292. https://doi.org/10.12989/scs.2019.32.2.281.
  59. Fazelzadeh, S.A., Rahmani, S., Ghavanloo, E. and Marzocca, P. (2019), "Thermoelastic vibration of doubly-curved nano-composite shells reinforced by graphene nanoplatelets", J. Thermal Stresses, 42(1), 1-17. https://doi.org/10.1080/01495739.2018.1524733.
  60. Ghadiri, M. and SafarPour, H. (2017), "Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment", J. Thermal Stresses, 40(1), 55-71. https://doi.org/10.1080/01495739.2016.1229145.
  61. Ghavanloo, E., Rafii-Tabar, H. and Fazelzadeh, S.A. (2019), "Modelling the mechanical characteristics of carbon nanotubes: A nonlocal differential approach", In Springer Tracts in Mechanical Engineering, PartF1, 187-217), https://doi.org/10.1007/978-3-030-11650-7_9.
  62. Gholami, R., Darvizeh, A., Ansari, R. and Sadeghi, F. (2016), "Vibration and buckling of first-order shear deformable circular cylindrical micro-/nano-shells based on Mindlin's strain gradient elasticity theory", Europ. J. Mech. A/Solids, 58, 76-88. https://doi.org/10.1016/j.euromechsol.2016.01.014.
  63. Ghorbanpour Arani, A., BabaAkbar Zarei, H. and Haghparast, E. (2018), "Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets", JVC/J. Vib. Control, 24(21), 5169-5185. https://doi.org/10.1177/1077546317747501.
  64. Ghorbanpour Arani, A., Haghparast, E. and BabaAkbar Zarei, H. (2017), "Vibration characteristics of axially moving titanium-polymer nanocomposite faced sandwich plate under initial tension", Int. J. Eng. Appl. Sci., 9(2), 39-39. https://doi.org/10.24107/ijeas.303299.
  65. Ghorbanpour Arani, A. and Zamani, M.H. (2018), "Nonlocal free vibration analysis of FG-porous shear and normal deformable sandwich nanoplate with Piezoelectric face sheets resting on silica aerogel foundation", Arab. J. Sci. Eng., 43(9), 4675-4688. https://doi.org/10.1007/s13369-017-3035-8.
  66. Griebel, M. and Hamaekers, J. (2004), "Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites", Comput. Meth. Appl. Mech. Eng., 193(17-20), 1773-1788. https://doi.org/10.1016/j.cma.2003.12.025.
  67. Han, Y. and Elliott, J. (2007), "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  68. Jermsittiparsert, K., Ghabussi, A., Forooghi, A., Shavalipour, A., Habibi, M., won Jung, D. and Safa, M. (2020), "Critical voltage, thermal buckling and frequency characteristics of a thermally affected GPL reinforced composite microdisk covered with piezoelectric actuator", Mech. Based Des. Struct. Machines. https://doi.org/10.1080/15397734.2020.1748052.
  69. Jeyaraj, P. and Rajkumar, I. (2013), "Static behavior of FG-CNT polymer nano composite plate under elevated non-uniform temperature fields", Procedia Eng., 64, 825-834. https://doi.org/10.1016/j.proeng.2013.09.158.
  70. Karami, B., Shahsavari, D., Ordookhani, A., Gheisari, P., Li, L. and Eyvazian, A. (2020), "Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions", Steel Compos. Struct., 36(6), 689. https://doi.org/10.12989/SCS.2020.36.6.689.
  71. Karimi, M. and Shahidi, A.R. (2017), "Thermo-mechanical vibration, buckling, and bending of orthotropic graphene sheets based on nonlocal two-variable refined plate theory using finite difference method considering surface energy effects", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 231(3), 111-130. https://doi.org/10.1177/2397791417719970.
  72. Khoddami Maraghi, Z., Amir, S. and Arshid, E. (2022), "On the natural frequencies of smart circular plates with magnetorheological fluid core embedded between magnetostrictive patches on Kerr elastic substance", Mech. Based Des. Struct. Machines, 1-18. https://doi.org/10.1080/15397734.2022.2156885.
  73. Khorasani, M., Soleimani-Javid, Z., Arshid, E., Amir, S. and Civalek, O . (2021), "Vibration analysis of graphene nanoplatelets' reinforced composite plates integrated by piezo-electromagnetic patches on the piezo-electromagnetic media", Waves Random Complex Media, 1-31. https://doi.org/10.1080/17455030.2021.1956017.
  74. Khorshidvand, A.R., Joubaneh, E.F., Jabbari, M. and Eslami, M. R. (2014), "Buckling analysis of a porous circular plate with piezoelectric sensor-actuator layers under uniform radial compression", Acta Mech., 225(1), 179-193. https://doi.org/10.1007/s00707-013-0959-2.
  75. Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers", Comput. Mathem. Appl., 72(9), 2433-2449. https://doi.org/10.1016/j.camwa.2016.09.007.
  76. Kiani, Y., Dimitri, R. and Tornabene, F. (2018), "Free vibration of FG-CNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation", Compos. Part B: Eng., 147, 169-177. https://doi.org/10.1016/j.compositesb.2018.04.028.
  77. Kiarasi, F., Asadi, A., Babaei, M., Asemi, K. and Hosseini, M. (2022), "Dynamic analysis of functionally graded carbon nanotube (FGCNT) reinforced composite beam resting on viscoelastic foundation subjected to impulsive loading", J. Comput. Appl. Mech., 53(1), 1-23. https://doi.org/10.22059/JCAMECH.2022.339008.693.
  78. Kolahdouzan, F., Arani, A.G. and Abdollahian, M. (2018), "Buckling and free vibration analysis of FG-CNTRC-micro sandwich plate", Steel Compos. Struct., 26(3), 273-287. https://doi.org/10.12989/scs.2018.26.3.273.
  79. Krizhevsky, G. and Stavsky, Y. (1996), "Refined theory for vibrations and buckling of laminated isotropic annular plates", Int. J. Mech. Sci., 38(5), 539-555. https://doi.org/10.1016/0020-7403(95)00053-4.
  80. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method", Compos. Struct., 98, 160-168. https://doi.org/10.1016/j.compstruct.2012.11.006.
  81. Leissa, A.W. (1967), "Vibration of a simply-supported elliptical plate", J. Sound Vib., 6(1), 145-148. https://doi.org/10.1016/0022-460X(67)90166-6
  82. Leissa, A.W. (1969), Vibration of Plates, OHIO STATE UNIV COLUMBUS.
  83. Li, L., Tang, H. and Hu, Y. (2018), "Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature", Compos. Struct., 184, 1177-1188. https://doi.org/10.1016/j.compstruct.2017.10.052.
  84. Li, X., Gao, H., Scrivens, W.A., Fei, D., Xu, X., Sutton, M.A., Reynolds, A.P. and Myrick, M.L. (2007), "Reinforcing mechanisms of single-walled carbon nanotube-reinforced polymer composites", J. Nanosci. Nanotechnol., 7(7), 2309-2317. https://doi.org/10.1166/jnn.2007.410.
  85. Liu, S., Yu, T. and Bui, T.Q. (2017), "Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis", Europ. J. Mech., A/Solids, 66, 446-458. https://doi.org/10.1016/j.euromechsol.2017.08.008.
  86. Liu, S., Yu, T., Bui, T.Q. and Xia, S. (2017a), "Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory", Compos. Struct., 172, 34-44. https://doi.org/10.1016/j.compstruct.2017.03.067.
  87. Liu, S., Yu, T., Bui, T.Q. and Xia, S. (2017b), "Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory", Compos. Struct., 172, 34-44. https://doi.org/10.1016/j.compstruct.2017.03.067.
  88. Loghman, A., Arani, A.G. and Barzoki, A.A.M. (2017), "Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates", Comput. Concrete, 19(6), 677-687. https://doi.org/10.12989/cac.2017.19.6.677.
  89. Malekzadeh, P. and Shojaee, M. (2013), "Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers", Thin-Wall. Struct., 71, 108-118. https://doi.org/10.1016/j.tws.2013.05.008.
  90. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020), "Investigating nonlinear forced vibration behavior of multi-phase nanocomposite annular sector plates using Jacobi elliptic functions", Steel Compos. Struct., 36(1), 87-101. https://doi.org/10.12989/scs.2020.36.1.087.
  91. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", Meccanica, 51(9), 2185-2201. https://doi.org/10.1007/s11012-015-0348-0.
  92. Mohammadimehr, M., Najafabadi, M.M.M., Nasiri, H. and Rousta Navi, B. (2016), "Surface stress effects on the free vibration and bending analysis of the nonlocal single-layer graphene sheet embedded in an elastic medium using energy method", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 230(3), 148-160. https://doi.org/10.1177/1740349914559042.
  93. Mousavi, S.B., Amir, S., Jafari, A. and Arshid, E. (2021), "Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories", Adv. Nano Res., 10(3), 235-251. https://doi.org/10.12989/anr.2021.10.3.235.
  94. Quan, T.Q., Ha, D.T.T. and Duc, N.D. (2022), "Analytical solutions for nonlinear vibration of porous functionally graded sandwich plate subjected to blast loading", Thin-Wall. Struct., 170, 108606. https://doi.org/10.1016/j.tws.2021.108606.
  95. Quang, V.D., Khoa, N.D. and Duc, N.D. (2021), "The effect of structural characteristics and external conditions on the dynamic behavior of shear deformable FGM porous plates in thermal environment", J. Mech. Sci. Technol., 35(8), 3323-3329. https://doi.org/10.1007/S12206-021-0706-X/METRICS.
  96. Seidel, G.D. and Lagoudas, D.C. (2006), "Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38(8-10), 884-907. https://doi.org/10.1016/j.mechmat.2005.06.029.
  97. Selim, B.A., Zhang, L.W. and Liew, K.M. (2016), "Vibration analysis of CNT reinforced functionally graded composite plates in a thermal environment based on Reddy's higher-order shear deformation theory", Compos. Struct., 156, 276-290. https://doi.org/10.1016/j.compstruct.2015.10.026.
  98. Sharifan, M.H. and Jabbari, M. (2020), "Mechanical buckling analysis of saturated porous functionally graded elliptical plates subjected to in-plane force resting on two parameters elastic foundation based on HSDT", J. Pressure Vessel Technol., Transact. ASME, 142(4). https://doi.org/10.1115/1.4046707.
  99. Stephanis, C.G., Mourmouras, D.E. and Tsagadopoulos, D.G. (2003), "On the elastic properties of arteries", J. Biomech., 36(11), 1727-1731. https://doi.org/10.1016/S0021-9290(03)00188-X.
  100. Tao, C. and Dai, T. (2021), "Isogeometric analysis for size-dependent nonlinear free vibration of graphene platelet reinforced laminated annular sector microplates", Europ. J. Mech. - A/Solids, 86, 104171. https://doi.org/10.1016/j.euromechsol.2020.104171.
  101. Thai, H.T. and Choi, D.H. (2013), "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Compos. Struct., 95, 142-153. https://doi.org/10.1016/j.compstruct.2012.08.023.
  102. Thanh, N. Van, Khoa, N.D., Tuan, N.D., Tran, P. and Duc, N.D. (2017), "Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations", J. Thermal Stresses, 40(10), 1254-1274. https://doi.org/10.1080/01495739.2017.1338928.
  103. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  104. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets", Compos. Part B: Eng., 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040.
  105. Wu, Q., Miao, W.S., Zhang, Y. Du, Gao, H.J. and Hui, D. (2020), "Mechanical properties of nanomaterials: A review", Nanotechnol. Rev., 9(1), 259-273. https://doi.org/10.1515/ntrev2020-0021.
  106. Yu, T., Hu, H., Zhang, J. and Bui, T.Q. (2019), "Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory", Thin-Wall. Struct., 138, 1-14. https://doi.org/10.1016/j.tws.2018.12.006.
  107. Zandekarimi, S., Asadi, B. and Rahaeifard, M. (2018), "Size dependent thermal buckling and postbuckling of functionally graded circular microplates based on modified couple stress theory", J. Thermal Stresses, 41(1), 1-16. https://doi.org/10.1080/01495739.2017.1364612.
  108. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B: Eng., 159, 231-247. https://doi.org/10.1016/J.COMPOSITESB.2018.09.051.
  109. Zenkour, A.M. and El-Shahrany, H.D. (2021), "Quasi-3D theory for the vibration and deflection of a magnetostrictive composite plate resting on a viscoelastic medium", Compos. Struct., 269, 114028. https://doi.org/10.1016/j.compstruct.2021.114028.
  110. Zenkour, A.M. and Sobhy, M. (2018), "Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin-Voigt viscoelastic nanoplate embedded in a viscoelastic medium", Acta Mechanica, 229(1), 3-19. https://doi.org/10.1007/s00707-017-1920-6.
  111. Zhu, P., Lei, Z.X. and Liew, K.M. (2012a), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010.
  112. Zhu, P., Lei, Z.X. and Liew, K.M. (2012b), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010.