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Vibration Analysis of Shearable Composite Annular Plates Reinforced by Graphene Nanoplatelets Using the Differential Quadrature Method

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Mechanics of Composite Materials Aims and scope

A numerical analysis of the vibration problem for the annular plates from functionally graded graphene-platelets-reinforced composites (FG-GPLRC) was carried out. Since the amount of reinforcing platelets was different in different layers of the plates, they had a stratified structure. Based on Mindlin’s theory of moderately thick plates, the differential quadrature method (DQM) was used to study their fundamental frequencies. The first five calculated natural frequencies showed that this method gives results rather well agreeing with data reported in the scientific literature. The natural frequencies of the composite annular plates were studied considering their different geometric parameters: ratios of their external dimensions, GPL weight fractions, GPL distribution patterns, and GPL dimension ratios.

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References

  1. L. Wang, W. C. Wang, Y. Fu, et al., “Enhanced electrical and mechanical properties of rubber/graphene film through layer-by-layer electrostatic assembly,” Compos. Part B-Eng., 90, 457-464 (2016).

    Article  CAS  Google Scholar 

  2. D. D. Evanoff and G. Chumanov, “Synthesis and optical properties of silver nanoparticles and arrays,” ChemPhysChem., 6, 1221-1231 (2005).

    Article  CAS  PubMed  Google Scholar 

  3. X. Q. Li, “Nonlinear vibration of graphene reinforced functionally graded beam,” M. D. Thesis (Jiangsu University, Jiangsu, 2018), [in Chinese].

  4. J. Yang, H. L. Wu, and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer graphene plateletreinforced composite beams,” Compos. Struct., 161, 111-118 (2017).

    Article  Google Scholar 

  5. M. T. Song, S. Kitipornchai, and J. Yang, “Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets,” Compos. Struct., 159, 579-588 (2017).

    Article  Google Scholar 

  6. Y. Niu, W. Zhang, and X. Y. Guo, “Free vibration of rotating pretwisted functionally graded composite cylindrical panel reinforced with graphene platelets,” Eur. J. Mech. A-SOLID, 77, 103798 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  7. K. I. Tzou, J. A. Wickert, and A. Akay, “In-plane vibration modes of arbitrarily thick disks,” J. Vib. Acoust., 120, No. 2, 384-391 (1998).

    Article  Google Scholar 

  8. C. I. Park, “Frequency equation for the in-plane vibration of a clamped circular plate,” J. Sound Vib., 313, No. 1-2, 3, 325-333 (2008).

  9. S. Bashmal, R. Bhat, and S. Rakheja, “In-plane free vibration of circular annular disks,” J. Sound Vib., 322, 216-226 (2009).

    Article  ADS  Google Scholar 

  10. S. Bashmal, R. Bhat, and S. Rakheja, “In-plane free vibration analysis of an annular disks with point elastic support,” Shock. Vib., 18, 627-640 (2011).

    Article  Google Scholar 

  11. A. Murat, “Free in-plane vibration of super-elliptical plates,” Shock. Vib., 18, 471-484 (2011).

    Article  Google Scholar 

  12. Y. Niu, M. H. Yao, and Q. L. Wu, “Resonance in dangerous mode and chaotic dynamics of a rotating pre-twisted graphene reinforced composite blade with variable thickness,” Compos. Struct., 288, 115422 (2022).

    Article  CAS  Google Scholar 

  13. Y. Niu, M. Q. Wu, M. H. Yao, and Q. L. Wu, “Dynamic instability and internal resonance of rotating pretwisted composite airfoil blades,” Chaos Solution. Fract., 165, 112835 (2022).

    Article  MathSciNet  Google Scholar 

  14. F. Allahkarami, “Dynamic buckling of functionally graded multilayer graphene nanocomposite annular plate under different boundary conditions in thermal environment,” Eng. Comput., 38, 583-606 (2022).

    Article  Google Scholar 

  15. F. Allahkarami and H. Tohidi, “Axisymmetric postbuckling of functionally graded graphene platelets reinforced composite annular plate on nonlinear elastic medium in thermal environment,” Int. J. Struct. Stab. Dy., 23, No. 03, 2350034 (2023).

  16. M. Safarpour, A. Rahimi, A. Alibeigloo, H. Bisheh, and A. Forooghi, “Parametric study of three-dimensional bending and frequency of FG-GPLRC porous circular and annular plates on different boundary conditions,” Mech. Based Des. Struct. Mach., 49, No. 5, 707-737 (2021).

    Article  Google Scholar 

  17. H. Bisheh, A. Alibeigloo, M. Safarpour, and A. R. Rahimi, “Three-dimensional static and free vibrational analysis of graphene reinforced composite circular/annular plate using differential quadrature method,” Int. J. Appl. Mech., 11, No. 08, 1950073 (2019).

  18. F. Allahkarami and H. Tohidi, “Size-dependent nonlinear free vibration of multilayer functionally graded graphene nanocomposite Timoshenko microbeam under different boundary conditions,” Eur. Phys. J. Plus, 137, No. 5 (2022).

  19. J. Torabi and R. Ansari, “Nonlinear free vibration analysis of thermally induced FG-CNTRC annular plates: Asymmetric versus axisymmetric study,” Comput. Methods Appl. Mech. Eng., 324, 327-347 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  20. J. -B. Han and K. M. liew, “Axisymmetric free vibration of thick annular plates,” Int. J. Mech. Sci., 41, 1089-1109 (1999).

  21. T. Irie, G. Yamada, and S. Aomura, “Free vibration of Mindlin annular plates of varying thickness,” J. Sound Vib., 66, No. 2, 187-197 (1979).

    Article  ADS  Google Scholar 

  22. T. Irie, G. Yamada, and K. Takagi, “Natural frequencies of thick annular plates,” J. Appl. Mech., 49, No. 3, 633-638 (1982).

    Article  ADS  Google Scholar 

  23. S. L. Nayar, K. K. Raju, and G. V. Rao, “Axisymmetric free vibrations of internally compressed moderately thick annular plates,” Comput. Struct., 53, No. 3, 759-765 (1994).

    Article  Google Scholar 

  24. C. W. Bert, S. K. Jang, and A. G. Striz, “Two new approximate methods for analyzing free vibration of structural components,” AIAAJ., 26, No. 5, 612-618 (1988).

    Article  ADS  Google Scholar 

  25. A. R. Kukreti, J. Farsa, and C. W. Bert, “Fundamental frequency of tapered plates by differential quadrature,” J. Eng. Mech., 118, No. 6, 1221-1237 (1992).

    Article  Google Scholar 

  26. X. Wang, A. G. Striz, and C. W. Bert, “Free vibration analysis of annular plates by the DQ method,” J. Sound Vib., 164, No. 1, 173-175 (1993).

    Article  ADS  Google Scholar 

  27. X. Wang, J. Yang, and J. Xiao, “On free vibration analysis of circular annular plates with non-uniform thickness by the differential quadrature method,” J. Sound Vib., 184, No. 3, 547-551 (1995).

    Article  ADS  Google Scholar 

  28. K. M. Liew, J.-B. Han, Z. M. Xiao, and H. Du, “Differential quadrature method for Mindlin plates on Winkler foundations,” Int. J. Mech. Sci., 38, No. 4, 405-421 (1996).

    Article  Google Scholar 

  29. R. D. Mindlin, “Influence of rotatory inertia and shear on flexural motion of isotropic, elastic plates,” J. Appl. Mech., 18, No. 1, 31-38 (1951).

    Article  ADS  Google Scholar 

  30. R. Gholami and R. Ansari, “Nonlinear stability and vibration of pre/post-buckled multilayer FG-GPLRPC rectangular plates,” Appl. Math. Model., 65, 627-660 (2019).

    Article  MathSciNet  Google Scholar 

  31. A. Wang, H. Chen, Y. Hao, et al., “Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets,” Results Phys., 9, 550-559 (2018).

    Article  ADS  Google Scholar 

  32. T. Li, Z. H. Qi, and X. Ma, “High order hybrid stress quadrilateral element for bending and vibration analysis of Mindlin plates,” J. Dalian Univ. Techno., 54, No. 5, 491-498 (2014). [in Chinese].

    Google Scholar 

  33. Q. L. Li, “Static and dynamic responses of functionally graded material beams and circular plates under follow-up loads,” Ph. D. Thesis (Lanzhou University of technology, Lanzhou (2012). [in Chinese].

  34. C. W. Bert and M. Malik, “Differential quadrature method in computational mechanics,” Appl. Mech. Rev., 49, 1-27 (1996).

    Article  ADS  Google Scholar 

  35. J. Yang, H. L. Wu, and S. Kitipornchai, “Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams,” Compos. Struct., 161, 111-118 (2017).

    Article  Google Scholar 

  36. T. Ramanathan, A. A. Abdala, S. Stankovich, D. A. Dikin, M. Herrera-Alonso, R. D. Piner et al., “Functionalized graphene sheets for polymer nanocomposites,” Nat. Nanotechnol., 3, No. 6 327-331 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  37. S. Kitipornchai, D. Chen, and J. Yang, “Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets,” Mater. Des., 116, 656-665 (2017).

    Article  CAS  Google Scholar 

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Acknowledgement

This work was supported by the National Natural Science Foundation of China (No. 12062010).

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Authors and Affiliations

  1. School of Civil Engineering, Lanzhou University of Technology, Lanzhou, 730050, P. R. China

    Q. Zhou

  2. School of Science, Lanzhou University of Technology, Lanzhou, 730050, P. R. China

    J. H. Zhang

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Correspondence to Q. Zhou.

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Zhou, Q., Zhang, J.H. Vibration Analysis of Shearable Composite Annular Plates Reinforced by Graphene Nanoplatelets Using the Differential Quadrature Method. Mech Compos Mater 60, 117–134 (2024). https://doi.org/10.1007/s11029-024-10178-2

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