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Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach

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Abstract

Based on Reddy’s third-order shear deformation theory and mixed formulation, a new numerical approach in the variational framework is developed to analyze the geometrically nonlinear free vibration behavior of cylindrical panels having cutouts with various shapes (e.g., square, circular, elliptical) under arbitrary boundary conditions. It is also assumed that the panel is made of functionally graded graphene platelet-reinforced composite with various patterns for the distribution of GPLs along the thickness direction whose effective properties are estimated using the modified Halpin–Tsai model in conjunction with the rule of mixture. The proposed approach can be named VDQFEM as it utilizes the VDQ and FE methods. Efficient matrix formulation, being free from the locking problem, computational efficiency and being able to solve problems with concave and polygon domains are the main features of VDQFEM. Selected numerical results are given to investigate the influences of geometrical parameters and weight fraction/distribution pattern of GPLs on the large-amplitude vibration response of panels with various cutouts and boundary conditions.

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References

  1. Ventsel, E., Krauthammer, T.: Thin Plates and Shells, Theory, Analysis and Applications. Marcel Dekker, New York (2001)

    Book  Google Scholar 

  2. Pietraszkiewicz, W., Gorski, J.: (eds.) Shell Structures: Theory and Applications. In: Proceedings of 10th SSTA Conference Poland (2013)

  3. Zingoni, A.: Shell structures in civil and mechanical engineering: theory and closed-form analytical solutions. Thomas Telford, London (1997)

    Book  Google Scholar 

  4. Moussaoui, F., Benamar, R.: Non-linear vibrations of shell-type structures: a review with bibliography. J. Sound Vib. 255, 161–184 (2002)

    Article  Google Scholar 

  5. Amabili, M., APaidoussis, M.P.: Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction. Appl. Mech. Rev. 56, 349–381 (2003)

    Article  Google Scholar 

  6. Alijani, F., Amabili, M.: Non-linear vibrations of shells: a literature review from 2003 to 2013. Int. J. Non-Linear Mech. 58, 233–257 (2014)

    Article  Google Scholar 

  7. Amabili, M., Reddy, : A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. Int. J. Non-linear Mech. 45, 409–418 (2010)

    Article  Google Scholar 

  8. Amabili, M.: A new third-order shear deformation theory with non-linearities in shear for static and dynamic analysis of laminated doubly curved shells. Compos. Struct. 128, 260–273 (2015)

    Article  Google Scholar 

  9. Amabili, M., Reddy, J.N.: The nonlinear, third-order thickness and shear deformation theory for statics and dynamics of laminated composite shells. Compos. Struct. 244, 112265 (2020)

    Article  Google Scholar 

  10. Kurpa, L., Pilgun, G., Amabili, M.: Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments. J. Sound Vib. 306, 580–600 (2007)

    Article  Google Scholar 

  11. Pilgun, G., Amabili, M.: Nonlinear vibrations of shallow circular cylindrical panels with complex geometry. Meshless discretization with the R-functions method. Int. J. Non-linear Mech. 47, 137–152 (2012)

    Article  Google Scholar 

  12. Ashrafi, B., Hubert, P., Vengallatore, S.: Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems. Nanotechnology 17, 4895 (2006)

    Article  Google Scholar 

  13. Esawi, A.M.K., Farag, M.M.: Carbon nanotube reinforced composites: potential and current challenges. Mater. Des. 28, 2394–2401 (2007)

    Article  Google Scholar 

  14. Loos, M.: Carbon nanotube reinforced composites. CNR Polym. Sci. Technol. (2015). https://doi.org/10.1016/C2012-0-06123-6

    Article  Google Scholar 

  15. Shi, G., Araby, S., Gibson, C.T., Meng, Q., Zhu, S., Ma, J.: Graphene platelets and their polymer composites: fabrication, structure, properties, and applications. Adv. Funct. Mater. 28, 1706705 (2018)

    Article  Google Scholar 

  16. Secor, E.B., Ahn, B.Y., Gao, T.Z., Lewis, J.A., Hersam, M.C.: Rapid and versatile photonic annealing of graphene inks for flexible printed electronics. Adv. Mater. 27, 6683 (2015)

    Article  Google Scholar 

  17. Gholami, R., Ansari, R.: Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Eng. Struct. 156, 197–209 (2018)

    Article  Google Scholar 

  18. Gholami, R., Ansari, R.: On the nonlinear vibrations of polymer nanocomposite rectangular plates reinforced by graphene nanoplatelets: a unified higher-order shear deformable model Iranian. Iranian J. Sci. Technol. Trans. Mech. Eng. 43, 603–620 (2019)

    Article  Google Scholar 

  19. Rao, M.N., Schmidt, R., Schröder, K.U.: Forced vibration analysis of FG-graphene platelet reinforced polymer composite shells bonded with piezoelectric layers considering electroelastic nonlinearities. In: ASME 2018 conference on smart materials, adaptive structures and intelligent systems, 1, pp. 10–12 (2011)

  20. Wang, Y., Xie, K., Fu, T., Shi, C.: Vibration response of a functionally graded graphene nanoplatelet reinforced composite beam under two successive moving masses. Compos. Struct. 209, 928–939 (2019)

    Article  Google Scholar 

  21. Wang, Y., Feng, C., Wang, X., Zhao, Z., Santiuste, C., Dong, Y.H., Yang, J.: Nonlinear static and dynamic responses of graphene platelets reinforced composite beam with dielectric permittivity. Appl. Math. Model. 71, 298–315 (2019)

    Article  MathSciNet  Google Scholar 

  22. Zhou, Z., Ni, Y., Tong, Z., Zhu, S., Sun, J., Xu, X.: Accurate nonlinear buckling analysis of functionally graded porous graphene platelet reinforced composite cylindrical shells. Int. J. Mech. Sci. 151, 537–550 (2019)

    Article  Google Scholar 

  23. Faghih Shojaei, M., Ansari, R.: Variational differential quadrature: a technique to simplify numerical analysis of structures. Appl. Math. Model. 49, 705–738 (2017)

    Article  MathSciNet  Google Scholar 

  24. Torabi, J., Ansari, R., Hassani, R.: 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 (2019)

    Article  MathSciNet  Google Scholar 

  25. Hassani, R., Ansari, R., Rouhi, H.: Large deformation analysis of 2D hyperelastic bodies based on the compressible nonlinear elasticity: a numerical variational method. Int. J. Non-Linear Mech. 116, 39–54 (2019)

    Article  Google Scholar 

  26. Hassani, R., Ansari, R., Rouhi, H.: A VDQ-based multifield approach to the 2D compressible nonlinear elasticity. Int. J. Numer. Meth. Eng. 118, 345–370 (2019)

    Article  MathSciNet  Google Scholar 

  27. Ansari, R., Hassani, R., Gholami, R., Rouhi, H.: Nonlinear bending analysis of arbitrary-shaped porous nanocomposite plates using a novel numerical approach. Int. J. Non-Linear Mech. 126, 103556 (2020)

    Article  Google Scholar 

  28. Ansari, R., Hassani, R., Gholami, R., Rouhi, H.: Thermal postbuckling analysis of FG-CNTRC plates with various shapes and temperature-dependent properties using the VDQ-FEM technique. Aerosp. Sci. Technol. 106, 106078 (2020)

    Article  Google Scholar 

  29. Affdl, J.H., Kardos, J.L.: The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16, 344–352 (1976)

    Article  Google Scholar 

  30. Hull, D., Clyne, T.: An Introduction to Composite Materials. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  31. Harris, B.: Engineering Composite Materials. The institute of Metals, London (1986)

    Google Scholar 

  32. Wu, H., Kitipornchai, S., Yang, J.: Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates. Mater. Des. 132, 430–441 (2017)

    Article  Google Scholar 

  33. Alibeigloo, A.: Three-dimensional free vibration analysis of multi-layered graphene sheets embedded in elastic matrix. J. Vib. Control 19, 2357–2371 (2013)

    Article  MathSciNet  Google Scholar 

  34. Wu, H., Drzal, L.T.: Effect of graphene nanoplatelets on coefficient of thermal expansion of polyetherimide composite. Mater. Chem. Phys. 146, 26–36 (2014)

    Article  Google Scholar 

  35. Reddy, J.N.: A simple higher-order theory for laminated composite plates ASME. ASME J. Appl. Mech. 51, 745–752 (1984)

    Article  Google Scholar 

  36. Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. CRC Press (2006)

    Book  Google Scholar 

  37. Keller, H.B.: Numerical solution of bifurcation and nonlinear eigenvalue problems, Appl. Bifurc. Theory, pp. 359–384 (1977)

  38. Hasrati, E., Ansari, R., Torabi, J.: A novel numerical solution strategy for solving nonlinear free and forced vibration problems of cylindrical shells. Appl. Math. Model. 53, 653–672 (2018)

    Article  MathSciNet  Google Scholar 

  39. Mirzaei, M., Kiani, Y.: Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels. Compos. Struct. 142, 45–56 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran

    R. Ansari, R. Hassani & E. Hasrati

  2. Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, Rasht, Iran

    R. Ansari

  3. Faculty of Engineering Science, Faculty of Technology and Engineering, University of Guilan, East of Guilan, P.C, 44891-63157, Rudsar-Vajargah, Iran

    H. Rouhi

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  1. R. Ansari
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  2. R. Hassani
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  4. H. Rouhi
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Correspondence to R. Ansari.

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Ansari, R., Hassani, R., Hasrati, E. et al. Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach. Acta Mech 232, 3417–3439 (2021). https://doi.org/10.1007/s00707-021-03000-w

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  • DOI: https://doi.org/10.1007/s00707-021-03000-w

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