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The influence of graphene platelet with different dispersions on the vibrational behavior of nanocomposite truncated conical shells

  • Khayat, Majid (Department of Civil and Environmental Engineering, Shiraz University of Technology) ;
  • Baghlani, Abdolhossein (Department of Civil and Environmental Engineering, Shiraz University of Technology) ;
  • Dehghan, Seyed Mehdi (Department of Civil and Environmental Engineering, Shiraz University of Technology) ;
  • Najafgholipour, Mohammad Amir (Department of Civil and Environmental Engineering, Shiraz University of Technology)
  • Received : 2020.06.04
  • Accepted : 2020.12.22
  • Published : 2021.01.10

Abstract

This work addresses the free vibration analysis of Functionally Graded Porous (FGP) nanocomposite truncated conical shells with Graphene PLatelet (GPL) reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin-Tsai equations are used to find the effective material properties of the graphene platelet reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders's theory. The Fourier Differential Quadrature (FDQ) technique is implemented to solve the governing equations of the problem and to obtain the natural frequencies of the truncated conical shell. The combination of FDQ with higher-order shear deformation theory allows a very accurate prediction of the natural frequencies. The precision and reliability of the proposed method are verified by the results of literature. Moreover, a wide parametric study concerning the effect of some influential parameters, such as the geometrical parameters, porosity distribution, circumferential wave numbers, GPLs dispersion as well as boundary restraint conditions on free vibration response of FGP-GPL truncated conical shell is also carried out and investigated in detail.

Keywords

Acknowledgement

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

References

  1. Abbaszadeh, M. and Dehghan, M. (2020), "An upwind local radial basis functions-differential quadrature (RBFs-DQ) technique to simulate some models arising in water sciences", Ocean Eng., 197, 106844. https://doi.org/10.1016/j.oceaneng.2019.106844.
  2. Abdollahzadeh Shahrbabaki, E. and Alibeigloo, A. (2014), "Three-dimensional free vibration of carbon nanotube-reinforced composite plates with various boundary conditions using Ritz method", Compos. Struct., 111, 362-370. https://doi.org/10.1016/j.compstruct.2014.01.013.
  3. Abediokhchi, J., Kouchakzadeh, M.A. and Shakouri, M. (2013), "Buckling analysis of cross-ply laminated conical panels using GDQ method", Compos,Part B: Eng., 55, 440-446. https://doi.org/10.1016/j.compositesb.2013.07.003.
  4. Akgun, G. and Kurtaran, H. (2018), "Geometrically nonlinear transient analysis of laminated composite super-elliptic shell structures with generalized differential quadrature method", Int. J. Nonlinear Mech., 105, 221-241. https://doi.org/10.1016/j.ijnonlinmec.2018.05.016.
  5. Ansari, R., Faghih Shojaei, M., Rouhi, H. and Hosseinzadeh, M. (2015), "A novel variational numerical method for analyzing the free vibration of composite conical shells", Appl. Math. Model., 39(10), 2849-2860. https://doi.org/10.1016/j.apm.2014.11.012.
  6. Arefi, M., Mohammad-Rezaei Bidgoli, E., Dimitri, R. and Tornabene, F. (2018), "Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Aerosp. Sci. Technol., 81, 108-117. https://doi.org/10.1016/j.ast.2018.07.036.
  7. Bacciocchi, M., Eisenberger, M., Fantuzzi, N., Tornabene, F. and Viola, E. (2016), "Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method", Compos. Struct., 156, 218-237. https://doi.org/10.1016/j.compstruct.2015.12.004.
  8. Baghlani, A., Khayat, M. and Dehghan, S.M. (2020), "Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction", Appl. Math.Model., 78, 550-575. https://doi.org/10.1016/j.apm.2019.10.023.
  9. Baghlani, A., Najafgholipour, M.A. and Khayat, M. (2020), "The influence of mechanical uncertainties on the free vibration of functionally graded graphene-reinforced porous nanocomposite shells of revolution", Eng. Struct., 111356. https://doi.org/10.1016/j.engstruct.2020.111356.
  10. Bai, X., Cao, D. and Zhang, H. (2020), "Simultaneously morphology and phase controlled synthesis of cobalt manganese hydroxides/reduced graphene oxide for high performance supercapacitor electrodes", Ceramics Int., 46(1), https://doi.org/10.1016/j.ceramint.2020.04.249.
  11. Behroozi, A.M. and Vaghefi, M. (2020), "Numerical simulation of water hammer using implicit Crank-Nicolson Local Multiquadric Based Differential Quadrature", Int. J. Press. Vess. Piping. 181, 104078. https://doi.org/10.1016/j.ijpvp.2020.104078.
  12. Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008.
  13. Chen, Y., Jin, G., Zhang, C., Ye, T. and Xue, Y. (2018), "Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory", Compos. Part B: Eng., 153, 376-386. https://doi.org/10.1016/j.compositesb.2018.08.111.
  14. Civalek, O. (2006), "Free vibration analysis of composite conical shells using the discrete singular convolution algorithm", Steel Compos.Struct., 6(4), 353-366. https://doi.org/10.12989/scs.2006.6.4.353.
  15. Clare, A.T., Reynolds, W.J., Murray, J.W., Aboulkhair, N.T., Simonelli, M., Hardy, M., Grant, D.M. and Tuck, C. (2020), "Laser calorimetry for assessment of melting behaviour in multi-walled carbon nanotube decorated aluminium by laser powder bed fusion", CIRP Annals, 69(1), https://doi.org/10.1016/j.cirp.2020.04.053.
  16. Daneshmand, F., Rafiei, M., Mohebpour, S.R. and Heshmati, M. (2013), "Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory", Appl. Math. Model., 37(16-17), 7983-8003. https://doi.org/10.1016/j.apm.2013.01.052.
  17. de Freitas, D.N., Mendonca, B.H.S., Kohler, M.H., Barbosa, M.C., Matos, M.J.S., Batista, R.J.C. and de Oliveira, A.B. (2020), "Water Diffusion in Carbon Nanotubes Under Directional Electric Fields: Coupling Between Mobility and Hydrogen Bonding", Chem. Phys., 537, 110849. https://doi.org/10.1016/j.chemphys.2020.110849.
  18. Dehnavi, A. and Soleymanpour, A. (2020), "Highly sensitive voltammetric electrode for the trace measurement of methyldopa based on a pencil graphite modified with phosphomolibdate/graphene oxide", Microchem. J., 157, 104969. https://doi.org/10.1016/j.microc.2020.104969.
  19. Di Sciuva, M. and Sorrenti, M. (2019), "Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory", Compos. Struct., 227, 111324. https://doi.org/10.1016/j.compstruct.2019.111324.
  20. Do, Q.C., Pham, D.N., Vu, D.Q., Vu, T.T.A. and Nguyen, D.D. (2019), "Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load", Steel Compos.Struct., 31(3), 243-259. https://doi.org/10.12989/scs.2019.31.3.243.
  21. Do, V.N.V. and Lee, C.H. (2018), "Quasi-3D higher-order shear deformation theory for thermal buckling analysis of FGM plates based on a meshless method", Aerosp. Sci. Technol., 82-83, 450-465. https://doi.org/10.1016/j.ast.2018.09.017.
  22. Dong, Y.H., Li, Y.H., Chen, D. and Yang, J. (2018), "Vibration characteristics of functionally graded graphene reinforced porous nanocomposite cylindrical shells with spinning motion", Compos.Part B: Eng., 145, 1-13. https://doi.org/10.1016/j.compositesb.2018.03.009.
  23. Ebrahimi, F., Seyfi, A., Dabbagh, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  24. Eyvazian, A., Hamouda, A.M., Tarlochan, F., Mohsenizadeh, S. and Dastjerdi, A.A. (2019), "Damping and vibration response of viscoelastic smart sandwich plate reinforced with non-uniform Graphene platelet with magnetorheological fluid core", Steel Compos. Struct., 33(6), 891-906. https://doi.org/10.12989/scs.2019.33.6.891.
  25. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs)", Compos. Part B: Eng., 110, 132-140. https://doi.org/10.1016/j.compositesb.2016.11.024.
  26. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs)", Eng. Struct., 140, 110-119. https://doi.org/10.1016/j.engstruct.2017.02.052.
  27. Gao, K., Do, D.M., Li, R., Kitipornchai, S. and Yang, J. (2020), "Probabilistic stability analysis of functionally graded graphene reinforced porous beams", Aerosp. Sci. Technol., 98, 105738. https://doi.org/10.1016/j.ast.2020.105738.
  28. Gautam, A.K., Faraz, M. and Khare, N. (2020), "Enhanced thermoelectric properties of MoS2 with the incorporation of reduced graphene oxide (RGO)", J. Alloys Compounds, 155673. https://doi.org/10.1016/j.jallcom.2020.155673.
  29. Gupta, A. and Talha, M. (2017), "Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment", Int. J. Struct. Stab. Dynam., 18(1), 1850013. https://doi.org/10.1142/S021945541850013X.
  30. Han, C., Li, Y., Wang, Q., Wen, S., Wei, Q., Yan, C., Hao, L., Liu, J. and Shi, Y. (2018), "Continuous functionally graded porous titanium scaffolds manufactured by selective laser melting for bone implants", J. Mech. Behavior Biomedical Mater., 80, 119-127. https://doi.org/10.1016/j.jmbbm.2018.01.013.
  31. Heydarpour, Y. and Aghdam, M.M. (2016), "A hybrid Bezier based multi-step method and differential quadrature for 3D transient response of variable stiffness composite plates", Compos. Struct., 154, 344-359. https://doi.org/10.1016/j.compstruct.2016.07.060.
  32. Heydarpour, Y., Aghdam, M.M. and Malekzadeh, P. (2014), "Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells", Compos. Struct., 117, 187-200. https://doi.org/10.1016/j.compstruct.2014.06.023.
  33. Hong, C.C. (2010), "Computational approach of piezoelectric shells by the GDQ method", Compos. Struct., 92(3), 811-816. https://doi.org/10.1016/j.compstruct.2009.08.026.
  34. Hosseini-Hashemi, S. and Ilkhani, M.R. (2016), "Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory", Compos. Struct., 157, 1-11. https://doi.org/10.1016/j.compstruct.2016.08.019.
  35. Hosseini, S.M. and Zhang, C. (2018), "Elastodynamic and wave propagation analysis in a FG graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel Compos. Struct., 27(3), 255-271. https://doi.org/10.12989/scs.2018.27.3.255.
  36. Hu, Y., Ji, W.M. and Zhang, L.W. (2020), "Water-induced Damage Revolution of the Carbon Nanotube Reinforced Poly (methyl methacrylate) Composites", Compos. Part A: Appl. Sci. Manufact., 105954. https://doi.org/10.1016/j.compositesa.2020.105954.
  37. Irie, T., Yamada, G. and Tanaka, K. (1984), "Natural frequencies of truncated conical shells", J. Sound Vib., 92(3), 447-453. https://doi.org/10.1016/0022-460X(84)90391-2
  38. Javani, M., Kiani, Y. and Eslami, M.R. (2019), "Free vibration of arbitrary thick FGM deep arches using unconstrained higher-order shear deformation theory", Thin-Wall. Struct., 136, 258-266. https://doi.org/10.1016/j.tws.2018.12.020.
  39. Javani, R., Bidgoli, M.R. and Kolahchi, R. (2019), "Buckling analysis of plates reinforced by Graphene platelet based on Halpin-Tsai and Reddy theories", Steel Compos. Struct., 31(4), 419-426. https://doi.org/10.12989/scs.2019.31.4.419.
  40. Kahkhaie, V.R., Yousefi, M.H., Darbani, S.M.R. and Mobashery, A. (2020), "Enhanced Raman Intensity of Pollutants and Explosives by Using 2-Mercaptoethanol Controlled Pyramid Ag-Iron Nanostructure Embedded Graphene Oxide Platform", Photonics and Nanostructures - Fundamentals and Applications. 100801. https://doi.org/10.1016/j.photonics.2020.100801.
  41. Kamali, M., Shamsi, M. and Saidi, A.R. (2018), "Surface effect on buckling of microtubules in living cells using first-order shear deformation shell theory and standard linear solid model", Mechanics Res. Commun., 92, 111-117. https://doi.org/10.1016/j.mechrescom.2018.08.011.
  42. Khandelwal, R.P. and Chakrabarti, A. (2015), "Calculation of interlaminar shear stresses in laminated shallow shell panel using refined higher order shear deformation theory", Compos. Struct., 124, 272-282. https://doi.org/10.1016/j.compstruct.2015.01.025.
  43. Khayat, M., Baghlani, A. and Dehghan, S.M. (2020), "A semi-analytical boundary method in investigation of dynamic parameters of functionally graded storage tank", J. Braz. Soc. Mech. Sci. Eng., 42(6), 332. https://doi.org/10.1007/s40430-020-02407-1.
  44. Khayat, M., Baghlani, A. and Najafgholipour, M.A. (2020), "The propagation of uncertainty in the geometrically nonlinear responses of smart sandwich porous cylindrical shells reinforced with graphene platelets", Compos. Struct., 113209. https://doi.org/10.1016/j.compstruct.2020.113209.
  45. Khayat, M., Dehghan Seyed, M., Najafgholipour Mohammad, A. and Baghlani, A. (2018), "Free vibration analysis of functionally graded cylindrical shells with different shell theories using semi-analytical method", Steel Compos. Struct., 28(6), 735-748. https://doi.org/10.12989/scs.2018.28.6.735.
  46. Khayat, M., Poorveis, D. and Moradi, S. (2016), "Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method", Steel Compos. Struct., 22(2), 301-321. https://doi.org/10.12989/scs.2016.22.2.301.
  47. Khayat, M., Poorveis, D. and Moradi, S. (2017), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Steel Compos. Struct., 23(1),1-16. https://doi.org/10.12989/scs.2017.23.1.001.
  48. Khayat, M., Poorveis, D. and Moradi, S. (2017), "Semi-Analytical Approach in Buckling Analysis of Functionally Graded Shells of Revolution Subjected to Displacement Dependent Pressure", J. Press. Vess. Technol., 139(6). https://doi.org/10.1115/1.4037042.
  49. Khayat, M., Poorveis, D., Moradi, S. and Hemmati, M. (2016), "Buckling of thick deep laminated composite shell of revolution under follower forces", Struct. Eng. Mech., 58(1), 59-91. https://doi.org/10.12989/sem.2016.58.1.059.
  50. Khayat, M., Rahnema, H., Baghlani, A. and Dehghan, S.M. (2019), "A theoretical study of wave propagation of eccentrically stiffened FGM plate on Pasternak foundations based on higher-order shear deformation plate theory", Mater. Today Commun., 20 100595. https://doi.org/10.1016/j.mtcomm.2019.100595.
  51. Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers", Comput. Math. Appl., 72(9), 2433-2449. https://doi.org/10.1016/j.camwa.2016.09.007.
  52. 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.
  53. Kieback, B., Neubrand, A. and Riedel, H. (2003), "Processing techniques for functionally graded materials", Mater. Sci. Eng.: A. 362(1-2), 81-106. https://doi.org/10.1016/S0921-5093(03)00578-1.
  54. Kim, J.I., Cho, J.S., Wang, D.H. and Park, J.H. (2020), "Highly dispersible graphene oxide nanoflakes in pseudo-gel-polymer porous separators for boosting ion transportation", Carbon, 166, https://doi.org/10.1016/j.carbon.2020.05.003.
  55. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  56. Korkmaz, A. and Dag, I. (2011), "Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation", J. Franklin Inst., 348(10), 2863-2875. https://doi.org/10.1016/j.jfranklin.2011.09.008.
  57. Kreja, I., Schmidt, R. and Reddy, J.N. (1997), "Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures", Int. J. Nonlinear Mech., 32(6), 1123-1142. https://doi.org/10.1016/S0020-7462(96)00124-2.
  58. Kurtaran, H. (2015), "Geometrically nonlinear transient analysis of moderately thick laminated composite shallow shells with generalized differential quadrature method", Compos. Struct., 125, 605-614. https://doi.org/10.1016/j.compstruct.2015.02.045.
  59. Lair, J., Hui, D., Sofiyev, A.H., Gribniak, V. and Turan, F. (2019), "On the parametric instability of multilayered conical shells using the FOSDT", Steel Compos. Struct., 31(3), 277-290. https://doi.org/10.12989/scs.2019.31.3.277.
  60. Lal, R. and Saini, R. (2020), "Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule", Appl. Acoust., 158, 107027. https://doi.org/10.1016/j.apacoust.2019.107027.
  61. Li, W.L. (2000), "Free vibrations of beams with general boundary conditions", J. Sound Vib., 237(4), 709-725. https://doi.org/10.1006/jsvi.2000.3150.
  62. Liew, K.M., Ng, T.Y. and Zhao, X. (2005), "Free vibration analysis of conical shells via the element-free kp-Ritz method", J. Sound Vib., 281(3), 627-645. https://doi.org/10.1016/j.jsv.2004.01.005.
  63. Lin, J., Zhao, Y., Watson, D. and Chen, C.S. (2020), "The radial basis function differential quadrature method with ghost points", Math. Comput. Simul., 173, 105-114. https://doi.org/10.1016/j.matcom.2020.01.006.
  64. Liu, C., Li, X., Li, R., Yang, Q., Zhang, H., Yang, B. and Yang, G. (2020), "Laser ignited combustion of graphene oxide/nitrocellulose membrane for solid propellant micro thruster and solar water distillation", Carbon, 166, https://doi.org/10.1016/j.carbon.2020.05.014.
  65. Liu, X., George, M.N., Park, S., Ii, A.L.M., Gaihre, B., Li, L., Waletzki, B.E., Terzic, A., Yaszemski, M.J. and Lu, L. (2020), "3D-Printed Scaffolds with Carbon Nanotubes for Bone Tissue Engineering: Fast and Homogeneous One-Step Functionalization", Acta Biomaterialia, 111, https://doi.org/10.1016/j.actbio.2020.04.047.
  66. Lu, Z., Yu, J., Yao, J. and Hou, D. (2020), "Experimental and molecular modeling of polyethylene fiber/cement interface strengthened by graphene oxide", Cement Concrete Compos., 112, 103676. https://doi.org/10.1016/j.cemconcomp.2020.103676.
  67. Malekzadeh, P. (2009), "A two-dimensional layerwise-differential quadrature static analysis of thick laminated composite circular arches", Appl. Math. Model., 33(4), 1850-1861. https://doi.org/10.1016/j.apm.2008.03.008.
  68. Malekzadeh, P., Setoodeh, A.R. and Shojaee, M. (2018), "Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method", Comput. Method. Appl. M., 340, 451-479. https://doi.org/10.1016/j.cma.2018.06.006.
  69. Matsukawa, Y., Ohura, S. and Umemura, K. (2020), "Effect on near-infrared absorption spectra of DNA/single-walled carbon nanotube (SWNT) complexes by adsorption of a blocking reagent", Colloids Surfaces B: Biointerfaces, 111072. https://doi.org/10.1016/j.colsurfb.2020.111072.
  70. Mehar, K. and Panda, S.K. (2016), "Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field", Compos. Struct., 143, 336-346. https://doi.org/10.1016/j.compstruct.2016.02.038.
  71. Mehditabar, A., Rahimi, G.H. and Fard, K.M. (2018), "Vibrational responses of antisymmetric angle-ply laminated conical shell by the methods of polynomial based differential quadrature and Fourier expansion based differential quadrature", Appl. Math. Comput., 320, 580-595. https://doi.org/10.1016/j.amc.2017.10.017.
  72. Mercan, K., Baltacioglu, A.K. and Civalek, O. (2018), "Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method", Compos. Struct., 186, 139-153. https://doi.org/10.1016/j.compstruct.2017.12.008.
  73. Mirzaei, M. and Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Compos. Struct., 142, 45-56. https://doi.org/10.1016/j.compstruct.2015.12.071.
  74. Mohammadkhani, R., Ramezanzadeh, M., Akbarzadeh, S., Bahlakeh, G. and Ramezanzadeh, B. (2020), "Graphene oxide nanoplatforms reduction by green plant-sourced organic compounds for construction of an active anti-corrosion coating; experimental/electronic-scale DFT-D modeling studies", Chem. Eng. J., 397, 125433. https://doi.org/10.1016/j.cej.2020.125433.
  75. Nemati, S., Lima, P.M. and Sedaghat, S. (2020), "Legendre wavelet collocation method combined with the Gauss-Jacobi quadrature for solving fractional delay-type integro-differential equations", Appl. Numer. Math., 149, 99-112. https://doi.org/10.1016/j.apnum.2019.05.024.
  76. Nezamoleslami, R. and Khadem, S.E. (2017), "Investigation of the vibration of lattice composite conical shells formed by geodesic helical ribs", Steel Compos. Struct., 24(2), 249-264. https://doi.org/10.12989/scs.2017.24.2.249.
  77. Niu, Y., Zhang, W. and Guo, X.Y. (2019), "Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets", Eur. J. Mech. - A/Solids, 77, 103798. https://doi.org/10.1016/j.euromechsol.2019.103798.
  78. Oliva, M., De Marchi, L., Vieira Sanches, M., Pires, A., Cuccaro, A., Baratti, M., Chiellini, F., Morelli, A., Freitas, R. and Pretti, C. (2020), "Atlantic and Mediterranean populations of the widespread serpulid Ficopomatus enigmaticus: Developmental responses to carbon nanotubes", Marine Pollut. Bull., 156, 111265. https://doi.org/10.1016/j.marpolbul.2020.111265.
  79. Patil, M.A. and Kadoli, R. (2020), "Differential quadrature solution for vibration control of functionally graded beams with Terfenol-D layer", Appl. Math. Model., 84, 137-157. https://doi.org/10.1016/j.apm.2020.03.035.
  80. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng: A, 362(1), 40-60. https://doi.org/10.1016/S0921-5093(03)00580-X.
  81. Rahmani, M., Mohammadi, Y. and Kakavand, F. (2019), "Vibration analysis of sandwich truncated conical shells with porous FG face sheets in various thermal surroundings", Steel Compos. Struct., 32(2), 239-252. https://doi.org/10.12989/scs.2019.32.2.239.
  82. Reddy, J.N. (1984), "A Simple Higher-Order Theory for Laminated Composite Plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  83. Selim, B.A., Yin, B.B. and Liew, K.M. (2018), "Impact analysis of CNT-reinforced composite plates integrated with piezoelectric layers based on Reddy's higher-order shear deformation theory", Compos. Part B: Eng., 136, 10-19. https://doi.org/10.1016/j.compositesb.2017.09.074.
  84. Shakouri, M. (2019), "Free vibration analysis of functionally graded rotating conical shells in thermal environment", Compos. Part B: Eng., 163, 574-584. https://doi.org/10.1016/j.compositesb.2019.01.007.
  85. Shao, W. and Wu, X. (2011), "Fourier differential quadrature method for irregular thin plate bending problems on Winkler foundation", Eng. Anal. Bound. Elem., 35(3), 389-394. https://doi.org/10.1016/j.enganabound.2010.09.011.
  86. Shi, Z., Yao, X., Pang, F. and Wang, Q. (2017), "A semi-analytical solution for in-plane free vibration analysis of functionally graded carbon nanotube reinforced composite circular arches with elastic restraints", Compos. Struct., 182, 420-434. https://doi.org/10.1016/j.compstruct.2017.09.045.
  87. Shu, C. and Chew, Y.T. (1997), "Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems", Commun. Numer. Method. Eng., 13(8), 643-653. https://doi.org/10.1002/(SICI)1099-0887(199708)13:8<643::AID-CNM92>3.0.CO;2-F.
  88. Sobhy, M. and Zenkour, A.M. (2019), "Vibration analysis of functionally graded graphene platelet-reinforced composite doubly-curved shallow shells on elastic foundations", Steel Compos. Struct., 33(3), 195-208. https://doi.org/10.12989/scs.2019.33.2.195.
  89. Sofiyev, A.H., Zerin, Z., Allahverdiev, B.P., Hui, D., Turan, F. and Erdem, H. (2017), "The dynamic instability of FG orthotropic conical shells within the SDT", Steel Compos. Struct., 25(5), 581-591. https://doi.org/10.12989/scs.2017.25.5.581.
  90. Song, M., Kitipornchai, S. and Yang, J. (2017), "Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Struct., 159, 579-588. https://doi.org/10.1016/j.compstruct.2016.09.070.
  91. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B: Eng., 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043.
  92. Sun, C., Li, W., Xu, Y., Hu, N., Ma, J., Cao, W., Sun, S., Hu, C., Zhao, Y. and Huang, Q. (2020), "Effects of carbon nanotubes on the toxicities of copper, cadmium and zinc toward the freshwater microalgae Scenedesmus obliquus", Aquatic Toxicology. 105504. https://doi.org/10.1016/j.aquatox.2020.105504.
  93. Tamilalagan, E., Akilarasan, M., Chen, S.M., Chen, T.W., Huang, Y.C., Hao, Q. and Lei, W. (2020), "A sonochemical assisted synthesis of hollow sphere structured tin (IV) oxide on graphene oxide sheets for the low-level detection of environmental pollutant mercury in biological samples and foodstuffs", Ultrasonics Sonochemistry, 67, 105164. https://doi.org/10.1016/j.ultsonch.2020.105164.
  94. Topal, U. (2013), "Pareto optimum design of laminated composite truncated circular conical shells", Steel Compos. Struct., 14(4), 397-408. https://doi.org/10.12989/scs.2013.14.4.397.
  95. Torabi, J., Ansari, R. and Hassani, R. (2019), "Numerical study on the thermal buckling analysis of CNT-reinforced composite plates with different shapes based on the higher-order shear deformation theory", Eur. J. Mech. - A/Solids, 73, 144-160. https://doi.org/10.1016/j.euromechsol.2018.07.009.
  96. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. Part B: Eng., 67, 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012.
  97. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Dimitri, R. (2015), "Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method", Thin-Wall. Struct., 97, 114-129. https://doi.org/10.1016/j.tws.2015.08.023.
  98. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2015), "Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method", Compos. Part B: Eng., 81, 196-230. https://doi.org/10.1016/j.compositesb.2015.07.012.
  99. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2018), "Mechanical behavior of damaged laminated composites plates and shells: Higher-order Shear Deformation Theories", Compos. Struct., 189, 304-329. https://doi.org/10.1016/j.compstruct.2018.01.073.
  100. Tornabene, F., Liverani, A. and Caligiana, G. (2012), "General anisotropic doubly-curved shell theory: A differential quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian", J. Sound Vib., 331(22), 4848-4869. https://doi.org/10.1016/j.jsv.2012.05.036.
  101. Tornabene, F., Liverani, A. and Caligiana, G. (2012), "Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using generalized differential quadrature method", Int. J. Mech. Sci., 61(1), 71-87. https://doi.org/10.1016/j.ijmecsci.2012.05.007.
  102. Tran, L.V., Ly, H.A., Lee, J., Wahab, M.A. and Nguyen-Xuan, H. (2015), "Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach", Int. J. Mech.Sci., 96-97, 65-78. https://doi.org/10.1016/j.ijmecsci.2015.03.003.
  103. Tu, T.M., Quoc, T.H. and Van Long, N. (2019), "Vibration analysis of functionally graded plates using the eight-unknown higher order shear deformation theory in thermal environments", Aerosp. Sci. Technol., 84, 698-711. https://doi.org/10.1016/j.ast.2018.11.010.
  104. Venkatachari, A., Natarajan, S. and Ganapathi, M. (2018), "Variable stiffness laminated composite shells - Free vibration characteristics based on higher-order structural theory", Compos. Struct., 188, 407-414. https://doi.org/10.1016/j.compstruct.2018.01.025.
  105. Wang, A., Chen, H., Hao, Y. and Zhang, W. (2018), "Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets", Results in Phys., 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062.
  106. Wang, J.G., Ren, L., Hou, Z. and Shao, M. (2020), "Flexible reduced graphene oxide/prussian blue films for hybrid supercapacitors", Chem.Eng. J., 397, 125521. https://doi.org/10.1016/j.cej.2020.125521
  107. Wang, Q., Shao, D. and Qin, B. (2018), "A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions", Compos. Struct., 184, 211-232. https://doi.org/10.1016/j.compstruct.2017.09.070.
  108. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003.
  109. Wang, Y.Q., Liu, Y.F. and Zu, J.W. (2019), "Size-Dependent Vibration of Circular Cylindrical Polymeric Microshells Reinforced with Graphene Platelets", Int. J. Appl. Mech., 11(4), 1950036. https://doi.org/10.1142/S1758825119500364.
  110. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  111. Watson, D.W., Karageorghis, A. and Chen, C.S. (2020), "The radial basis function-differential quadrature method for elliptic problems in annular domains", J. Comput. Appl. Math., 363, 53-76. https://doi.org/10.1016/j.cam.2019.05.027.
  112. Winiarski, J.P., Rampanelli, R., Bassani, J.C., Mezalira, D.Z. and Jost, C.L. (2020), "Multi-walled carbon nanotubes/nickel hydroxide composite applied as electrochemical sensor for folic acid (vitamin B9) in food samples", J. Food Compos. Anal., 103511. https://doi.org/10.1016/j.jfca.2020.103511.
  113. Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Design, 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025.
  114. Wu, H., Yang, J. and Kitipornchai, S. (2017), "Dynamic instability of functionally graded multilayer graphene nanocomposite beams in thermal environment", Compos. Struct., 162, 244-254. https://doi.org/10.1016/j.compstruct.2016.12.001.
  115. Wu, H., Zhu, J., Kitipornchai, S., Wang, Q., Ke, L.L. and Yang, J. (2020), "Large amplitude vibration of functionally graded graphene nanocomposite annular plates in thermal environments", Compos. Struct., 239, 112047. https://doi.org/10.1016/j.compstruct.2020.112047.
  116. Wu, M., Ge, S., Jiao, C., Yan, Z., Jiang, H., Zhu, Y., Dong, B., Dong, M. and Guo, Z. (2020), "Improving electrical, mechanical, thermal and hydrophobic properties of waterborne acrylic resin-glycidyl methacrylate (GMA) by adding multi-walled carbon nanotubes", Polymer, 200, 122547. https://doi.org/10.1016/j.polymer.2020.122547.
  117. Xu, D., Liang, H., Zhu, X., Yang, L., Luo, X., Guo, Y., Liu, Y., Bai, L., Li, G. and Tang, X. (2020), "Metal-polyphenol dual crosslinked graphene oxide membrane for desalination of textile wastewater", Desalination, 487, 114503. https://doi.org/10.1016/j.desal.2020.114503.
  118. Yan, K., Zhang, Y., Cai, H. and Tahouneh, V. (2020), "Vibrational characteristic of FG porous conical shells using Donnell's shell theory", Steel Compos. Struct., 35(2), 249-260. https://doi.org/10.12989/scs.2020.35.2.249.
  119. Yang, D., Shen, J., Fan, J., Chen, Y. and Guo, X. (2020), "Paracellular Permeability Changes Induced by Multi-walled Carbon Nanotubes in Brain Endothelial Cells and Associated Roles of Hemichannels", Toxicology, 440, 152491. https://doi.org/10.1016/j.tox.2020.152491.
  120. Yang, F., Liu, X., Zhang, H., Zhou, J., Jiang, J. and Lu, X. (2020), "Boosting oxygen catalytic kinetics of carbon nanotubes by oxygen-induced electron density modulation for advanced Zn-Air batteries", Energy Storage Mater., 30, 138-145. https://doi.org/10.1016/j.ensm.2020.05.005.
  121. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090.
  122. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048.
  123. Yang, Z., Liu, A., Yang, J., Fu, J. and Yang, B. (2020), "Dynamic buckling of functionally graded graphene nanoplatelets reinforced composite shallow arches under a step central point load", J. Sound Vib., 465, 115019. https://doi.org/10.1016/j.jsv.2019.115019.
  124. Ye, F., Zhang, Z., Mi, Y., Huang, Z., Yuan, H., Zhang, Z. and Luo, Y. (2020), "Carbon nanotubes grafted with β-cyclodextrin by an ultrasonication method and its demulsification performance in oily wastewater", Colloids and Surfaces A: Physicochemical and Engineering Aspects. 600, 124939. https://doi.org/10.1016/j.colsurfa.2020.124939.
  125. Zghal, S., Frikha, A. and Dammak, F. (2018), "Free vibration analysis of carbon nanotube-reinforced functionally graded composite shell structures", Appl. Math. Model., 53, 132-155. https://doi.org/10.1016/j.apm.2017.08.021.
  126. Zhang, B., Li, H., Kong, L., Shen, H. and Zhang, X. (2020), "Size-dependent static and dynamic analysis of Reddy-type microbeams by strain gradient differential quadrature finite element method", Thin-Wall. Struct., 148, 106496. https://doi.org/10.1016/j.tws.2019.106496.
  127. Zhang, B., Li, H., Kong, L., Zhang, X. and Shen, H. (2020), "Strain gradient differential quadrature Kirchhoff plate finite element with the C2 partial compatibility", Eur. J. Mech. - A/Solids, 80, 103879. https://doi.org/10.1016/j.euromechsol.2019.103879.
  128. Zhang, G. and Zhu, R. (2020), "Runge-Kutta convolution quadrature methods with convergence and stability analysis for nonlinear singular fractional integro-differential equations", Commun. Nonlinear Scie. Numer. Simul., 84, 105132. https://doi.org/10.1016/j.cnsns.2019.105132.
  129. Zhang, W., Wnag, D.M. and Yao, M.H. (2014), "Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam", Nonlinear Dynam., 78(2), 839-856. https://doi.org/10.1007/s11071-014-1481-3.
  130. Zhang, X.Y., Fang, G., Leeflang, S., Zadpoor, A.A. and Zhou, J. (2019), "Topological design, permeability and mechanical behavior of additively manufactured functionally graded porous metallic biomaterials", Acta Biomaterialia, 84, 437-452. https://doi.org/10.1016/j.actbio.2018.12.013.
  131. Zhang, X.X., Zhang, J.F., Liu, Z.Y., Gan, W.M., Hofmann, M., Andra, H., Xiao, B.L. and Ma, Z.Y. (2020), "Microscopic stresses in carbon nanotube reinforced aluminum matrix composites determined by in-situ neutron diffraction", J. Mater. Sci. Technol., 54, 58-68. https://doi.org/10.1016/j.jmst.2020.04.016.
  132. Zhang, Y., Wang, H., Qian, P., Zhou, Y., Shi, J. and Shi, H. (2020), "Sulfonated poly(ether ether ketone)/amine-functionalized graphene oxide hybrid membrane with various chain lengths for vanadium redox flow battery: A comparative study", J. Membrane Sci., 610, 118232. https://doi.org/10.1016/j.memsci.2020.118232.
  133. Zhang, Y.M., Mirfakhraei, P., Xu, B. and Redekop, D. (1998), "A computer program for the elastostatics of a toroidal shell using the differential quadrature method", Int. J. Press. Vess. Piping, 75(13), 919-929. https://doi.org/10.1016/S0308-0161(98)00092-1.
  134. Zhao, J., Choe, K., Shuai, C., Wang, A. and Wang, Q. (2019), "Free vibration analysis of functionally graded carbon nanotube reinforced composite truncated conical panels with general boundary conditions", Compos. Part B: Eng., 160, 225-240. https://doi.org/10.1016/j.compositesb.2018.09.105.
  135. Zhao, S., Yang, Z., Kitipornchai, S. and Yang, J. (2020), "Dynamic instability of functionally graded porous arches reinforced by graphene platelets", Thin-Wall. Struct., 147, 106491. https://doi.org/10.1016/j.tws.2019.106491.
  136. Zhao, Z., Feng, C., Wang, Y. and Yang, J. (2017), "Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)", Compos. Struct., 180, 799-808. https://doi.org/10.1016/j.compstruct.2017.08.044.
  137. Zhou, X., Liu, X., Zhang, J., Zhang, C., Yoo, S.J., Kim, J.-G., Chu, X., Song, C., Wang, P., Zhao, Z., Li, D., Zhang, W. and Zheng, W. (2020), "Highly-dispersed cobalt clusters decorated onto nitrogen-doped carbon nanotubes as multifunctional electrocatalysts for OER, HER and ORR", Carbon, 166, 284-290. https://doi.org/10.1016/j.carbon.2020.05.037.
  138. Zhu, C., Mahmood, Z., Zhang, W., Akram, M.W., Ainur, D. and Ma, H. (2020), "In situ investigation of acute exposure of graphene oxide on activated sludge: Biofilm characteristics, microbial activity and cytotoxicity", Ecotoxicol. Environ. Saf.. 199, 110639. https://doi.org/10.1016/j.ecoenv.2020.110639.
  139. Zielnica, J. (2012), "Buckling and stability of elastic-plastic sandwich conical shells", Steel Compos. Struct., 13(2), 157-169. https://doi.org/10.12989/scs.2012.13.2.157.