Steel and Composite Structures

  • 제34권2호
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  • Pages.215-226
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  • 2020
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Vibration analysis of FG porous rectangular plates reinforced by graphene platelets

  • Zhou, Changlin (School of Civil Engineering and Mechanics, Huazhong University of Science and Technology) ;
  • Zhang, Zhongxian (School of Civil Engineering and Mechanics, Huazhong University of Science and Technology) ;
  • Zhang, Ji (School of Civil Engineering and Mechanics, Huazhong University of Science and Technology) ;
  • Fang, Yuan (General Construction Company of CCTEB Group Co.) ;
  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • 투고 : 2019.09.19
  • 심사 : 2019.12.02
  • 발행 : 2020.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

The research described in this paper was financially supported by the National Natural Science Foundation of China (No. 51378377) and National Natural Science Foundation of China (No. 41872001).

참고문헌

  1. Ahmed Houari, M.S., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/scs.2018.28.1.013.
  2. Alibeigloo, A. (2013), "Three-dimensional free vibration analysis of multi-layered graphene sheets embedded in elastic matrix", J.V.C., 19(16), 2357-2371. https://doi.org/10.1177/1077546312456056.
  3. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. http://dx.doi.org/10.12989/scs.2015.18.3.659.
  4. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091.
  5. Bennai, R., AitAtmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  6. Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mater., 6(2), 147-157. https://doi.org/10.1016/0167-6636(87)90005-6.
  7. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Review., 49(1), 1-28. https://doi.org/10.1115/1.3101882
  8. Bonnet, P., Sireude, D., Garnier, B. and Chauvet, O. (2007), "Thermal properties and percolation in carbon nanotube-polymer composites", J. Appl. Phys., 91(20), 2019-2030. https://doi.org/10.1063/1.2813625.
  9. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493.
  10. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. http://dx.doi.org/10.12989/scs.2015.19.3.679.
  11. Chang, T. and Gao, H. (2003), "Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model", J. Mech. Phys. Solids, 51(6), 1059-1074. https://doi.org/10.1016/S0022-5096(03)00006-1.
  12. Chen, C.H. and Cheng, C.H. (1996), "Effective elastic moduli of misoriented short-fiber composites", Int. J. Solids Struct., 33(17), 2519-2539. https://doi.org/10.1016/0020-7683(95)00160-3.
  13. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251.
  14. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  15. Cheng, Z.Q. and Batra, R. (2000), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates", J. Sound Vib., 229(4), 879-895. https://doi.org/10.1006/jsvi.1999.2525.
  16. Endo, M., Hayashi, T., Kim, Y.A., Terrones, M. and Dresselhaus, M.S. (2004), "Applications of carbon nanotubes in the twenty-first century", Philos. T. R. Soc. Lond., Series A: Mathematical, Physical and Engineering Sciences, 362, 2223-2238. https://doi.org/10.1098/rsta.2004.1437.
  17. Esawi, A.M. 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.
  18. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", Proc. R. Soc. London, Ser. A., 241(1226), 376-396. https://doi.org/10.1098/rspa.1957.0133.
  19. Eshelby, J.D. (1959), "The elastic field outside an ellipsoidal inclusion", Proc. R. Soc. London, Ser. A., 252(1271), 561-569. https://doi.org/10.1098/rspa.1959.0173.
  20. Fidelus, J., Wiesel, E., Gojny, F., Schulte, K. and Wagner, H. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A: Appl. Sci. Manuf., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006.
  21. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329(10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  22. Fung, Y.C. and Tong, P. (2001), "Classical and computational solid mechanics", 5, World scientific Singapore.
  23. Giordano, S., Palla, P. and Colombo, L. (2009), "Nonlinear elasticity of composite materials",Eur. Phys. J. B. Condensed Matter and Complex systems, 68(89), 89-101. https://doi.org/10.1140/epjb/e2009-00063-1.
  24. Han, Y. and Elliott, J. (2007)m "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.
  25. Hassan, M., Marin, M., Ellahi, R. and Alamri, S.Z. (2018), "Exploration of convective heat transfer and flow characteristics synthesis by Cu-Ag/water hybrid-nanofluids", Heat Transfer Res., 49(18), 1837-1848. DOI: 10.1615/HeatTransRes.2018025569.
  26. 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. http://dx.doi.org/10.12989/scs.2018.27.3.255.
  27. Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proc. R. Soc. London, Ser. A, 461(2058), 1685-1710. https://doi.org/10.1098/rspa.2004.1422.
  28. Jabbari, M., Hashemitaheri, M., Mojahedin, A., Eslami, M.R. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stresses, 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768.
  29. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2013), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140, 287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663.
  30. Jin, Y. and Yuan, F. (2003), "Simulation of elastic properties of single-walled carbon nanotubes", Compos. Sci. Technol., 63(11), 1507-1515. https://doi.org/10.1016/S0266-3538(03)00074-5.
  31. Kitipornchai, S., Chen, D., 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
  32. Liew, K.M., Han, J.B., Xiao, Z. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundations", Int. J. Mech. Sci., 38(4), 405-421. https://doi.org/10.1016/0020-7403(95)00062-3.
  33. Liu, F., Ming, P. and Li, J., (2007), "Ab initio calculation of ideal strength and phonon instability of graphene under tension", Physical Review B., 76, 064120. https://doi.org/10.1103/PhysRevB.76.064120.
  34. Liu, R. and Wang, L. (2015), "Thermal vibration of a single-walled carbon nanotube predicted by semiquantum molecular dynamics", Physical Chemistry Chemical Physics, 7.
  35. Marin, M., Agarwal, R.P. and Mahmoud, S.R. (2013), "Nonsimple material problems addressed by the Lagrange's identity", Bound. Value Probl., 135, 1-14. https://doi.org/10.1186/1687-2770-2013-135.
  36. Marin, M., Baleanu, D. and Vlase, S. (2017), "Effect of microtemperatures for micropolar thermoelastic bodies", Struct. Eng. Mech., 61(3), 381-387. https://doi.org/10.12989/sem.2017.61.3.381.
  37. Marin, M. and Craciun, E.M. (2017), "Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials", Compos. Part B: Eng., 126, 27-37. https://doi.org/10.1016/j.compositesb.2017.05.063.
  38. Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech.-ASCE, 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27).
  39. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  40. Moniruzzaman, M. and Winey, K.I. (2006), "Polymer nanocomposites containing carbon nanotubes", Macromolecules, 39(16), 5194-5205. https://doi.org/10.1021/ma060733p.
  41. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos.Struct., 22(2), 277-299. http://dx.doi.org/10.12989/scs.2016.22.2.277.
  42. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3.
  43. Mura, T. (1987), Micromechanics of defects in solids, 3, Springer Science & Business Media.
  44. Odegard, G., Gates, T., Wise, K., Park, C. and Siochi, E. (2003), "Constitutive modeling of nanotube-reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0.
  45. Othman, M.I.A. and Marin, M. (2017), "Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory", Results in Physics, 7, 3863-3872. https://doi.org/10.1016/j.rinp.2017.10.012.
  46. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  47. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites", Appl. Phys. Lett., 76, 2868-2870. https://doi.org/10.1063/1.126500@apl.2019.APLCLASS2019.issue-1.
  48. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS nano. 3, 3884-3890. https://doi.org/10.1021/nn9010472.
  49. Salvetat-Delmotte, J.P. and Rubio, A. (2002), "Mechanical properties of carbon nanotubes: a fiber digest for beginners", Carbon, 40(10), 1729-1734. https://doi.org/10.1016/S0008-6223(02)00012-X.
  50. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  51. Shen, H.S. (2012), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells", Compos. Part B: Eng., 43(3), 1030-1038. https://doi.org/10.1016/j.compositesb.2011.10.004.
  52. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Des., 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.
  53. Shen, H.S. and Zhu, Z.H. (2010), "Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments", Comput. Mater. Continua (CMC), 18(2), 155-182.
  54. Shu, C. and Wang, C. (1999), "Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates", Eng. Struct., 21(2), 125-134. https://doi.org/10.1016/S0141-0296(97)00155-7.
  55. Tahouneh, V. (2016), "Using an equivalent continuum model for 3D dynamic analysis of nanocomposite plates", Steel Compos. Struct., 20(3), 623-649. https://doi.org/10.12989/scs.2016.20.3.623.
  56. Tahouneh, V., Yas, M.H., Tourang, H. and Kabirian, M. (2013) "Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges", Meccanica, 48(6), 1313-1336. https://doi.org/10.1007/s11012-012-9669-4.
  57. Thostenson, E.T., Ren, Z. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 61(13), 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X.
  58. Tornabene, F., Bacciocchi, M., Fantuzzi, N. and Reddy, J.N. (2018), "Multiscale Approach for Three-Phase CNT/Polymer/Fiber Laminated Nanocomposite Structures", Polymer Composites, In Press, DOI: 10.1002/pc.24520.
  59. Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E. (2015), "Strong formulation finite element method based on differential quadrature: A survey", Appl. Mech. Rev., 67(2), 1-55. https://doi.org/10.1115/1.4028859.
  60. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2019), "Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis", Eng. Anal. Bound. Elem., 100, 24-47. https://doi.org/10.1016/j.enganabound.2017.07.029.
  61. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater., 21(1), 320-365. https://doi.org/10.1177/1099636217693623.
  62. Valter, B., Ram, M.K. and Nicolini, C. (2002), "Synthesis of multiwalled carbon nanotubes and poly (o-anisidine) nanocomposite material: Fabrication and characterization of its Langmuir-Schaefer films", Langmuir, 18(5), 1535-1541. https://doi.org/10.1021/la0104673.
  63. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  64. Wernik, J. and Meguid, S. (2011), "Multiscale modeling of the nonlinear response of nano-reinforced polymers", Acta Mech., 217(1), 1-16. https://doi.org/10.1007/s00707-010-0377-7
  65. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos.Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161.
  66. Xu, W., Wang, L. and Jiang, J. (2016), "Strain gradient finite element analysis on the vibration of double-layered graphene sheets", Int. J. Comput.Methods, 13(3). https://doi.org/10.1142/S0219876216500110.
  67. Yas, M.H. and Aragh, B.S. (2010), "Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation", Int. J. Eng. Sci., 48(12), 1881-1895. https://doi.org/10.1016/j.ijengsci.2010.06.015.
  68. Yokozeki, T., Iwahori, Y. and Ishiwata, S. (2007), "Matrix cracking behaviors in carbon fiber/epoxy laminates filled with cup-stacked carbon nanotubes (CSCNTs)", Compos. Part A: Appl. Sci. Manufact., 38(3), 917-924. https://doi.org/10.1016/j.compositesa.2006.07.005.
  69. Zhang, Y. and Wang, L. (2018), "Thermally stimulated nonlinear vibration of rectangular single-layered black phosphorus", J. Appl. Phys., 124(13), 10.1063/1.5047584. https://doi.org/10.1063/1.5047584

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