Structural Engineering and Mechanics

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Free vibration of FG-GPLRC conical panel on elastic foundation

  • Eyvazian, Arameh (Mechanical and Industrial Engineering Department, Qatar University) ;
  • Musharavati, Farayi (Mechanical and Industrial Engineering Department, Qatar University) ;
  • Tarlochan, Faris (Mechanical and Industrial Engineering Department, Qatar University) ;
  • Pasharavesh, Abdolreza (Mechanical Engineering Department, Sharif University of Technology) ;
  • Rajak, Dipen Kumar (Department of Mechanical Engineering, Sandip Institute of Technology and Research Center) ;
  • Husain, Mohammed Bakr (Department of Biological and Environmental Sciences, Qatar University) ;
  • Tran, Tron Nhan (Division of Computational Mechatronic, Institute for Computational Science, Ton Duc Thang University)
  • Received : 2019.12.17
  • Accepted : 2020.02.04
  • Published : 2020.07.10
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Abstract

Present research is aimed to investigate the free vibration behavior of functionally graded (FG) nanocomposite conical panel reinforced by graphene platelets (GPLs) on the elastic foundation. Winkler-Pasternak elastic foundation surrounds the mentioned shell. For each ply, graphaene platelets are randomly oriented and uniformly dispersed in an isotropic matrix. It is assumed that the Volume fraction of GPLs reainforcement could be different from layer to layer according to a functionally graded pattern. The effective elastic modulus of the conical panel is estimated according to the modified Halpin-Tsai rule in this manuscript. Cone is modeled based on the first order shear deformation theory (FSDT). Hamilton's principle and generalized differential quadrature (GDQ) approach are also used to derive and discrete the equations of motion. Some evaluations are provided to compare the natural frequencies between current study and some experimental and theoretical investigations. After validation of the accuracy of the present formulation and method, natural frequencies and the corresponding mode shapes of FG-GPLRC conical panel are developed for different parameters such as boundary conditions, GPLs volume fraction, types of functionally graded and elastic foundation coefficients.

Keywords

Acknowledgement

This research is founded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.99-2019.02.

References

  1. Affdl, J.H. and Kardos, J.L. (1976), "The HalpinTsai equations: a review", Polym. Eng. Sci., 16(5), 344-352. https://doi.org/10.1002/pen.760160512.
  2. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel. Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  3. Anirudh, B., Ganapathi, M., Anant, C. and Polit, O. (2019), "A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling", Compos. Struct., 222, p.110899. https://doi.org/10.1016/j.compstruct.2019.110899.
  4. Bao, S., Wang, S. (2019), "A unified procedure for free transverse vibration of rectangular and annular sectorial plates", Arch. Appl. Mech., 89(8), 1485-1499. https://doi.org/10.1007/s00419-019-01519-y.
  5. Bardell, N. S., Dunsdon, J. M., and Langley, R. S. (1998), "Free vibration of thin, isotropic, open, conical panels". J. Sound. Vib., 217(2), 297-320. https://doi.org/10.1006/jsvi.1998.1761.
  6. Cadelano, E., Palla, P.L., Giordano, S. and Colombo, L. (2009), "Nonlinear elasticity of monolayer graphene", Phys. Rev. Lett., 102(23), 235502. https://doi.org/10.1103/PhysRevLett.102.235502.
  7. Chandra, Y., Chowdhury, R., Scarpa, F., Adhikari, S., Sienz, J., Arnold, C., Murmu, T. and Bould, D. (2012), "Vibration frequency of graphene based composites: a multiscale approach", Mat. Sci. Eng. B-Adv., 177(3), 303-310. https://doi.org/10.1016/j.mseb.2011.12.024.
  8. Civalek, O. (2006), "Free vibration analysis of composite conical shells using the discrete singular convolution algorithm", Steel. Compos. Struct., 6(4), 353. https://doi.org/10.12989/scs.2006.6.4.353.
  9. Civalek, O. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct. Eng. Mech., 25(1), 127-130. https://doi.org/10.12989/sem.2007.25.1.127.
  10. Civalek, O., and Acar, M. H. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Int. J. Press. Vessel. Pip., 84(9), 527-535. https://doi.org/10.1016/j.ijpvp.2007.07.001.
  11. Civalek, O. (2008), "Vibration analysis of conical panels using the method of discrete singular convolution", Commun. Numer. Meth. Eng., 24(3), 169-181. https://doi.org/10.1002/cnm.961.
  12. Civalek, O. (2009), "Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method", Appl. Math. Model., 33(10), 3825-3835. https://doi.org/10.1016/j.apm.2008.12.019.
  13. Dong, Y.H., Zhu, B., Wang, Y., Li, Y.H. and Yang, J. (2018a), "Nonlinear free vibration of graded graphene reinforced cylindrical shells: Effects of spinning motion and axial load", J. Sound. Vib., 437, 79-96. https://doi.org/10.1016/j.jsv.2018.08.036.
  14. Dong, Y.H., Li, Y.H., Chen, D. and Yang, J. (2018b), "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.
  15. 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.
  16. Gao, K., Gao, W., Chen, D. and Yang, J. (2018), "Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation", Compos. Struct., 204, 831-846. https://doi.org/10.1016/j.compstruct.2018.08.013.
  17. Gholami, R. and Ansari, R. (2018), "Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates", Eng. Struct., 156, 197-209. https://doi.org/10.1016/j.engstruct.2017.11.019.
  18. Gholami, R. and Ansari, R. (2019), "Nonlinear stability and vibration of pre/post-buckled multilayer FG-GPLRPC rectangular plates", Appl. Math. Model., 65, 627-660. https://doi.org/10.1016/j.apm.2018.08.038.
  19. Guo, H., Cao, S., Yang, T. and Chen, Y. (2018), "Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method", Int. J. Mech. Sci., 142, 610-621. https://doi.org/10.1016/j.ijmecsci.2018.05.029.
  20. Javani, M., Kiani, Y., and Eslami, M. R. (2019), "Nonlinear axisymmetric response of temperature-dependent FGM conical shells under rapid heating", Acta Mech., 230(9), 3019-3039. https://doi.org/10.1007/s00707-019-02459-y.
  21. Javani, M., Kiani, Y., and Eslami, M. R. (2020), "Thermal buckling of FG graphene platelet reinforced composite annular sector plates", Thin. Wall. Struct., 148, p. 106589. https://doi.org/10.1016/j.tws.2019.106589.
  22. Javed, S., Viswanathan, K. K., Aziz, Z. A., and Lee, J. H. (2016), "Vibration analysis of a shear deformed anti-symmetric angle-ply conical shells with varying sinusoidal thickness", Struct. Eng. Mech., 58(6), 1001-1020. https://doi.org/10.12989/sem.2016.58.6.1001
  23. Kiani, Y. (2018), "Isogeometric large amplitude free vibration of graphene reinforced laminated plates in thermal environment using NURBS formulation", Comput. Method. Appl. M., 332, 86-101. https://doi.org/10.1016/j.cma.2017.12.015.
  24. Kiani, Y., Dimitri, R., and Tornabene, F. (2018), "Free vibration study of composite conical panels reinforced with FG-CNTs". Eng. Struct., 172, 472-482. https://doi.org/10.1016/j.engstruct.2018.06.006.
  25. Kiani, Y., And Mirzaei, M. (2019). "Isogeometric thermal postbuckling of FG-GPLRC laminated plates", Steel and Compos. Struct., 32(6), 821-832. https://doi.org/10.12989/scs.2019.32.6.821.
  26. 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.
  27. Kulkarni, Dhaval D., Ikjun Choi, Srikanth S. Singamaneni, and Vladimir V. Tsukruk. (2010) "Graphene oxide-polyelectrolyte nanomembranes", ACS. Nano., 4(8) 4667-4676. https://doi.org/10.1021/nn101204d.
  28. Liu, D., Kitipornchai, S., Chen, W. and Yang, J. (2018), "Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell", Compos. Struct., 189, 560-569. https://doi.org/10.1016/j.compstruct.2018.01.106.
  29. 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.
  30. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A.A. (2004), "Electric field effect in atomically thin carbon films", Science, 306(5696), 666-669. https://doi.org/1126/science.1102896. https://doi.org/10.1126/science.1102896
  31. Potts, J.R., Dreyer, D.R., Bielawski, C.W. and Ruoff, R.S. (2011), "Graphene-based polymer nanocomposites", Polymer, 52(1), 5-25. https://doi.org/10.1016/j.polymer.2010.11.042.
  32. 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(12), 3884-3890. https://doi.org/10.1021/nn9010472.
  33. Rahmani, M., Mohammadi, Y., & 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.
  34. Reddy, C.D., Rajendran, S. and Liew, K.M. (2006), "Equilibrium configuration and continuum elastic properties of finite sized graphene", Nanotechnology, 17(3), p.864. https://doi.org/10.1088/0957-4484/17/3/042.
  35. Reddy, J.N., (2006), Theory and analysis of elastic plates and shells, CRC press.
  36. Saidi, A.R., Bahaadini, R. and Majidi-Mozafari, K. (2019), "On vibration and stability analysis of porous plates reinforced by graphene platelets under aerodynamical loading", Compos. Part. B-Eng., 164, 778-799. https://doi.org/10.1016/j.compositesb.2019.01.074.
  37. Scarpa, F., Adhikari, S. and Phani, A.S. (2009), "Effective elastic mechanical properties of single layer graphene sheets", Nanotechnology, 20(6), p.065709. https://doi.org/10.1088/0957-4484/20/6/065709
  38. Shen, H.S., Lin, F. and Xiang, Y. (2017a), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations in thermal environments", Nonlinear. Dynam., 90(2), 899-914. https://doi.org/10.1007/s11071-017-3701-0.
  39. Shen, H.S., Xiang, Y. and Lin, F. (2017b), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated plates in thermal environments", Comput. Method. Appl. M., 319, 175-193. https://doi.org/10.1016/j.cma.2017.02.029.
  40. Shen, H.S., Xiang, Y. and Fan, Y. (2017c), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments", Compos. Struct., 182, 447-456. https://doi.org/10.1016/j.compstruct.2017.09.010.
  41. Shen, H.S., Xiang, Y., Fan, Y. and Hui, D. (2018), "Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical panels resting on elastic foundations in thermal environments", Compos. Part. B-Eng., 136, 177-186. https://doi.org/10.1016/j.compositesb.2017.10.032.
  42. Shen, H.S., Xiang, Y. and Fan, Y. (2019a), "Nonlinear vibration of thermally postbuckled FG-GRC laminated beams resting on elastic foundations", Int. J. Struct. Stab. Dy., 25(9), 1507-1520. https://doi.org/10.1142/S0219455419500512.
  43. Shen, H.S., Xiang, Y. and Fan, Y. (2019b), "Vibration of thermally postbuckled FG-GRC laminated plates resting on elastic foundations", J. Vib. Control., 19(6), p.1950051. https://doi.org/10.1177/1077546319825671.
  44. Shi, D.Y., Wang, Q.S., Shi, X.J., Pang, F.Z. (2015), "A series solution for the in-plane vibration analysis of orthotropic rectangular plates with non-uniform elastic boundary constraints and internal line supports", Arch. Appl. Mech., 81(1), 51-73. https://doi.org/10.1007/s00419-014-0899-x
  45. 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.
  46. Stankovich, S., Dikin, D.A., Dommett, G.H., Kohlhaas, K.M., Zimney, E.J., Stach, E.A., Piner, R.D., Nguyen, S.T. and Ruoff, R.S. (2006), "Graphene-based composite materials", Nature, 442(7100), p.282. https://doi.org/10.1038/nature04969
  47. Tornabene, F., Viola, E., & Inman, D. J. (2009), "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures", J. Sound. Vib., 328(3), 259-290. https://doi.org/10.1016/j.jsv.2009.07.031.
  48. Wang, M., Xu, Y.G., Qiao, P. and Li, Z.M. (2019a), "A two-dimensional elasticity model for bending and free vibration analysis of laminated graphene-reinforced composite beams", Compos. Struct., 211, 364-375. https://doi.org/10.1016/j.compstruct.2018.12.033.
  49. Wang, Y., Xie, K., Fu, T. and Shi, C. (2019b), "Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses", Compos. Struct., 209, 928-939. https://doi.org/10.1016/j.compstruct.2018.11.014.
  50. 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. Phys., 9, 550-559. https://doi.org/10.1016/j.rinp.2018.02.062.
  51. 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.
  52. Zhang, Y.Y., Wang, C.M., Cheng, Y. and Xiang, Y. (2011), "Mechanical properties of bilayer graphene sheets coupled by sp3 bonding", Carbon, 49(13), 4511-4517. https://doi.org/10.1016/j.carbon.2011.06.058.
  53. Zhao, X., Zhang, Q., Chen, D. and Lu, P. (2010), "Enhanced mechanical properties of graphene-based poly (vinyl alcohol) composites", Macromolecules, 43(5), 2357-2363. https://doi.org/10.1021/ma902862u.
  54. 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.