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A numerical study on free vibration analysis of detailed and homogenized models for FG-CNTRC beams

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Abstract

The goal of this study is to compare and investigate the free vibration characteristics of detailed and homogenized models for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams, based on the finite element method (FEM). In this study, three types of FG-CNTRC beams and boundary conditions are considered for different volume fractions of CNT: UD (uniformly distributed), FG-X, and FG-Λ beams. These beams in which single-walled carbon nanotubes (SWCNTs) are distributed with a gradient through the thickness are employed and analyzed for simply supported (SS), clamped-clamped (CC), and free-free (FF) boundary conditions. For the homogenized model, the effective material properties are determined in terms of the CNT volume fraction using the linear rule of mixture. A commercial midas NFX program is used for finite element simulations to analyze the free vibration responses of FG-CNTRC beams. The numerical results are compared with the existing analytical solutions in the literature in order to validate the developed finite element models.

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References

  1. N. D. Duc, Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi (2014).

    Google Scholar 

  2. J. N. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59 (2011) 2382–2399.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. H. Yas and N. Samadi, Free vibrations and buckling analysis of carbon nanotube-reinforced composite timoshenko beams on elastic foundation, International Journal of Pressure Vessels and Piping, 98 (2012) 119–128.

    Article  Google Scholar 

  4. A. Ghorbani Shenas, P. Malekzadeh and S. Ziaee, Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment, Composite Structures, 162 (2017) 325–340.

    Article  Google Scholar 

  5. N. D. Duc, T. Q. Quan and N. D. Khoa, New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced somposite double curved shallow shells subjected to blast load and temperature, Aerospace Science and Technology, 71 (2017) 360–372.

    Article  Google Scholar 

  6. N. D. Duc and P. P. Minh, Free vibration analysis of cracked FG CNTRC plates using phase field theory, Aerospace Science and Technology, 112 (2021) 106654.

    Article  Google Scholar 

  7. N. V. Thanh, N. D. Khoa, N. D. Tuan, P. Tran and N. D. Duc, Nonlinear dynamic response and vibration of functionally graded carbon-reinforced composite 9FG-CNTRC0 shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations, Journal of Thermal Stressess, 40 (1) (2017) 1254–1274.

    Article  Google Scholar 

  8. A. Karamanli and T. P. Vo, Finite element model for carbon nanotube-reinforced and graphene nanoplatelet-reinforced composite beams, Composite Structures, 264 (2021) 113739.

    Article  Google Scholar 

  9. N. D. Dat, N. V. Thanh, V. M. Anh and N. D. Duc, Vibration and nonlinear dynamic analysis of sandwich FG-CNTEC plate with porous core layer, Mechanics of Advanced Materials and Structures, 29 (10) (2022) 1431–1448.

    Article  Google Scholar 

  10. J. R. Cho, Free vibration analysis of functionally graded sandwich plates with a homogeneous core, Applied Sciences, 12 (2022) 6054.

    Article  Google Scholar 

  11. S. Yang, S. Yu and M. Cho, A study on the development of multiscale bridging method consideringthe particle size and concentration effect of nanocomposites, Journal of the Computational Structural Engineering Institute of Korea, 22 (4) (2009) 343–348.

    Google Scholar 

  12. H. S. Shen and C. L. Zhang, Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates, Materials and Design, 31 (7) (2010) 3403–3411.

    Article  Google Scholar 

  13. J. R. Cho and J. T. Oden, Functionally graded material: a parametric study on thermal-stress characteristics using the Crank-Nicolson-Galerkin scheme, Computer Methods in Applied Mechanics and Engineering, 188 (1–3) (2000) 17–38.

    Article  MATH  Google Scholar 

  14. J. R. Cho and D. Y. Ha, Averaging and finite-element discretizing approaches in the numerical analysis of functionally graded materials, Materials Science and Engineering A, 302 (2001) 187–196.

    Article  Google Scholar 

  15. T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21 (5) (1973) 571–574.

    Article  Google Scholar 

  16. R. Hill, A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, 13 (4) (1965) 213–222.

    Article  Google Scholar 

  17. K. S. Ravichandran, Elastic properties of two-phase composites, Journal of the American Ceramic Society, 77 (5) (1994) 1178–1184.

    Article  Google Scholar 

  18. MIDAS, Analysis Manual — Midas NFX, Modelling, Integrated Design and Analysis Software, Gyeonggi-do, South Korea (2020).

  19. H.-S. Shen and Y. Xiang, Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments, Engineering Structures, 56 (2013) 698–708.

    Article  Google Scholar 

  20. R. Ansari, M. Faghih Shojaei, V. Mohammadi, R. Gholami and F. Sadeghi, Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams, Composite Structures, 113 (2014) 316–327.

    Article  Google Scholar 

  21. Z. Shi, X. Yao, F. Pang and Q. Wang, An exact solution for the free-vibration analysis of functionally graded carbon-nanotube-reinforced composite beams with arbitrary boundary conditions, Scientific Reports, 7 (2017) 12909.

    Article  Google Scholar 

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1A2C110029).

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Authors and Affiliations

  1. Department of Mechanical Engineering, University College London, London, WC1E 7JE, UK

    Hyeong Jin Kim

  2. Department of Naval Architecture and Ocean Engineering, Hongik University, Sejong, 30016, Korea

    Jin-Rae Cho

Authors
  1. Hyeong Jin Kim
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  2. Jin-Rae Cho
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Correspondence to Jin-Rae Cho.

Additional information

Hyeong Jin Kim received his B.S. and M.S. degrees from the Hongik University and Pusan National University in 2020 and 2022, respectively. He is currently a Ph.D. student at the Department of Mechanical Engineering in University College London. His major research field is the nonlinear structural mechanics, analysis, and design of ships and offshore structures.

Jin-Rae Cho received his B.S. degree in Aeronautical Engineering from Seoul National University in 1983. He then received his M.S. and Ph.D. degrees from the University of Texas at Austin in 1993 and 1995, respectively. He is currently a Professor at the Department of Naval Architecture and Ocean Engineering in Hongik University. His major research field is the computational mechanics in solid/structural mechanics, ocean engineering and materials science.

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Kim, H.J., Cho, JR. A numerical study on free vibration analysis of detailed and homogenized models for FG-CNTRC beams. J Mech Sci Technol 37, 229–238 (2023). https://doi.org/10.1007/s12206-022-1224-1

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  • DOI: https://doi.org/10.1007/s12206-022-1224-1

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