Skip to main content
Log in

Dynamic Response of a Grid-Stiffened Composite Cylindrical Shell Reinforced with Carbon Nanotubes to a Radial Impulse Load

  • Published:
Mechanics of Composite Materials Aims and scope

Equilibrium equations of a rib grid-stiffened composite cylindrical shell reinforced with carbon nanotubes (CNTs) are derived based on the first-order shear deformation theory considering the effect of shear deformation and moment of inertia. The distribution of CNTs across the shell thickness is assumed uniform, and the elastic modulus of the CNT-reinforced polymer is calculated using the rule of mixtures. In order to determine the equivalent stiffness of the grid-stiffened composite cylindrical shell, the smeared stiffness method is used. Equilibrium equations for free and forced vibration of the rib grid-stiffened composite cylindrical shell are solved using the Galerkin method, and the effects of grid ribs on the dynamic response of the shell are investigated. The results found indicate that the use of circumferential ribs in the structure can increase the frequency, change the fundamental mode shape, and reduce the radial displacement by ~ 12% (especially in higher modes). In addition, the results demonstrate that a 5-degree increase in the angle of helical ribs can decrease the radial displacement linearly by 5%. Eventually, the corresponding outcomes reveal that the rib thickness and presence of CNTs may significantly increase the natural frequencies and decrease the radial displacement of such shells.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.

Similar content being viewed by others

References

  1. S. M. R. Khalili, R. Azarafza, and A. Davar, “Transient dynamic response of initially stressed composite circular cylindrical shells under radial impulse load,” Composite Structures, 89, No. 2, 275-284 (2009).

    Article  Google Scholar 

  2. X. M. Zhang, G. R. Liu, and K. Y. Lam, “Vibration analysis of thin cylindrical shells using wave propagation approach,” Sound and Vibration, 239, No. 3, 397-403. (2001).

    Article  Google Scholar 

  3. G. Jin, T. Ye, X. Ma, Y. Chen, Z. Su, and X. Xie, “A unified approach for the vibration analysis of moderately thick composite laminated cylindrical shells with arbitrary boundary conditions,” International Journal of Mechanical Sciences, 75, 357-376 (2013).

    Article  Google Scholar 

  4. M. Mirzaei and Y. Kiani, “Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout,” Beilstein Journal of Nanotechnology, 7, 511-523 (2016).

    Article  CAS  Google Scholar 

  5. L. W. Zhang, Z. X. Lei, and K. M. Liew, “Free vibration analysis of functionally graded carbon nanotube-reinforced composite triangular plates using the FSDT and element-free IMLS-Ritz method,” Composite. Structure, 120, 189-199 (2015).

    Article  Google Scholar 

  6. D. D. Nguyen, Q. Q. Tran, and D. K. Nguyen, “New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature,” Aerospace Science and Technology, 71, 360-372 (2017).

    Article  Google Scholar 

  7. L. W. Zhang, Z. G. Song, P. Qiao, and K. M. Liew, “Modeling of dynamic responses of CNT-reinforced composite cylindrical shells under impact loads,” Computer Methods in Applied Mechanics and Engineering, 313, 889-903 (2017).

    Article  Google Scholar 

  8. K. Mehar, S.K. Panda, and T.R. Mahapatra, “Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure,” International Journal of Mechanical Sciences, 133, 319- 329 (2017).

    Article  Google Scholar 

  9. A. Montazeri, J. Javadpour, A. Khavandi, A. Tcharkhtchi, and A. Mohajeri, “Mechanical properties of multi-walled carbon nanotube/epoxy composites,” Materials & Design, 31, No. 9, 4202-4208 (2010).

  10. Q. Jiang, X. Wang, Y. Zhu, D. Hui, and Y. Qiu, “Mechanical, electrical and thermal properties of aligned carbon nanotube/ polyimide composites,” Composite. Part B: Engineering, 56, 408-412 (2014).

    Article  CAS  Google Scholar 

  11. K. t. Lau, C. Gu, and D. Hui, “A critical review on nanotube and nanotube/nanoclay related polymer composite materials,” Composites Part B: Engineering, 37, No. 6, 425-436 (2006).

  12. W. Li, A. Dichiara, J. Zha, Z. Su, and J. Bai, “On improvement of mechanical and thermo-mechanical properties of glass fabric/epoxy composites by incorporating CNT–Al2O3 hybrids,” Composites Science and Technology, 103, 36-43 (2014).

    Article  CAS  Google Scholar 

  13. B. R. Redd, K. Ramji, and B. Satyanarayana, “Free vibration analysis of carbon nano-tube reinforced laminated composite panels,” World Academy of Science, Engineering and Technology, 5, No. 8, 1616-1620 (2011).

  14. P. Zhu, Z. X. Lei, and K. M. Liew, “Static and free vibration analyses of carbon nano-tubereinforced composite plates using finite element method with first-order shear deformation plate theory,” Composite Structure, 94, No. 4, 1450-1460 (2012).

  15. H. Zhang, F. Sun, H. Fan, H. Chen, L. Chen, and D. Fang, “Free vibration behaviors of carbon fiber reinforced latticecore sandwich cylinder,” Composites Science and Technology, 100, 26-33 (2014).

    Article  CAS  Google Scholar 

  16. Z. G. Song, L. W. Zhang, and K. M. Liew, “Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments,” International Journal of Mechanical Sciences, 115-116, 339-347 (2016).

    Article  Google Scholar 

  17. Z. G. Song, L. W. Zhang, and K. M. Liew, “Active vibration control of CNT reinforced functionally graded plates based on a higher-order shear deformation theory,” International Journal of Mechanical Sciences, 105, 90-101 (2016).

    Article  Google Scholar 

  18. J. H. Woo, J. H. Rho, and Lee, “Thermal buckling characteristics of composite conical shell structures,” International Journal of Aeronautical and Space Sciences, 8, No. 2, 82-88 (2007).

  19. S. K. Sahu, M. K. Rath, P. K. Datta, and R. Sahoo, “Parametric resonance characteristics of laminated composite curved shell panels in a hygrothermal environment,” International Journal of Aeronautical and Space Sciences, 13, No. 3, 332-348 (2012).

  20. Y. Kim, P. Kim, H. Kim, and J. Park, “Optimal design of a composite lattice rectangular plate for solar panels of a higagility satelite,” International Journal of Aeronautical and Space Sience, 19, 762-775 (2018).

    Article  Google Scholar 

  21. P. S. Harvey Jr and L. N. Virgin, “Effect of stiffener geometry on the response of grid-stiffened panels,” Journal of Engineering Mechanics, 144, No. 2, 06017021 (2017).

  22. J. Sun, C. W. Lim, X. Xu, and H. Mao, “Accurate buckling solutions of grid-stiffened functionally graded cylindrical shells under compressive and thermal loads,” Composites Part B: Engineering, 89, 96-107 (2016).

    Article  Google Scholar 

  23. Z. X. Lei, K. M. Liew, and J. L. Yu, “Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment,” Composite Structures, 106, 128-138 (2013).

    Article  Google Scholar 

  24. M. H. Yas and M. Heshmati, “Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load,” Applied Mathematical Modelling, 36, No. 4, 1371-1394 (2012).

  25. M. Yas, A. Pourasghar, S. Kamarian, and M. Heshmati, “Three-dimensional free vibration analysis of functionally graded nanocomposite cylindrical panels reinforced by carbon nanotube,” Materials & Design, 49, 583-590 (2013).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  27. P. Malekzadeh and A. R. Zarei, “Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers,” Thin-Walled Structures, 82, 221-232 (2014).

    Article  Google Scholar 

  28. N.D. Duc, H. Hadavinia, P. V. Thu, and T.Q. Quan, “Vibration and nonlinear dynamic response of imperfect three-phase polymer nanocomposite panel resting on elastic foundations under hydrodynamic loads,” Composite Structures, 131, 229-237 (2015).

    Article  Google Scholar 

  29. S. Kamarian, M. Salim, R. Dimitri, and F. Tornabene, “Free vibration analysis of conical shells reinforced with agglomerated carbon nanotubes,” International Journal of Mechanical Sciences, 108-109, 157-165 (2016).

  30. K. Torabi, M. Shariati-Nia, and M. Heidari-Rarani, “Experimental and theoretical investigation on transverse vibration of delaminated cross-ply composite beams,” International Journal of Mechanical Sciences, 115-116, 1-11 (2016).

    Article  Google Scholar 

  31. M. Shakouri and M. Kouchakzadeh, “Analytical solution for vibration of generally laminated conical and cylindrical shells,” International Journal of Mechanical Sciences, 131-132, 414-425 (2017).

    Article  Google Scholar 

  32. N. Fantuzzi, F. Tornabene, M. Bacciocchi, and R. Dimitri, “Free vibration analysis of arbitrarily shaped functionally graded carbon nanotube-reinforced plates,” Composites Part B: Engineering, 115, 384-408 (2017).

    Article  CAS  Google Scholar 

  33. N. Jaunky, N. F. Knight Jr, and D. R. Ambur, “Formulation of an improved smeared stiffener theory for buckling analysis of grid-stiffened composite panels,” Composites Part B: Engineering, 27, 519-526 (1996).

    Article  Google Scholar 

  34. S. Kidane, G. Li, J. Helms, S.-S. Pang, and E. Woldesenbet, “Buckling load analysis of grid-stiffened composite cylinders,” Composites Part B: Engineering, 34, No. 1, 1-9 (2003).

  35. M. Hemmatnezhad, G. H. Rahimi, and R. Ansari, “On the free vibrations of grid-stiffened composite cylindrical shells,” Acta Mechanica, 225, 609-623 (2014).

    Article  Google Scholar 

  36. D. Wang, M. M.Abdalla, Z-Pei Wang, and Z. Su, “Streamline stiffener path optimization SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures,” Computer Methods in Applied Mechanics and Engineering, 344, 1021-1050 (2019)

  37. R. Azarafza, A. Davar, M. S. Fayez, and J. E. Jam,. “Free vibration of grid-stiffened composite cylindrical shell reinforced with carbon nanotubes,” Mechanics of Composite Materials, 56, 505-522 (2020)

    Article  CAS  Google Scholar 

  38. H. S. Shen, “Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axiallyloaded shells,” Composite Structures, 93, No. 8, 2096-2108 (2011).

  39. Y. S. Lee and K. D. Lee, “On the dynamic response of laminated circular cylindrical shells under impulse loads,” Computers & Structures, 63, No. 1, 149-157 (1997).

  40. M. Zarei and G. H. Rahimi, “Free vibration analysis of rotating grid-stiffened composite cylindrical shells,” Modares Mechanical Engineering, 16, No. 9, 175-185 (2016).

  41. S. Khalili, K. Malekzadeh, A. Davar, and P. Mahajan, “Dynamic response of pre-stressed fibre metal laminate (FML) circular cylindrical shells subjected to lateral pressure pulse loads,” Composite Structures, 92, No. 6, 1308-1317 (2010).

  42. K.Y. Lam and C.T. Loy, “Influence of boundary conditions for a thin laminated rotating cylindrical shell,” Composite Structures, 41, No. 3-4, 215-228 (1998).

  43. R. F. Gibson, Principles of Composite Material Mechanics, CRC Press, Taylor & Francis Group, Boca Raton–London–New York (2016).

    Book  Google Scholar 

  44. D. Wang and M.M. Abdalla, “Global and local buckling analysis of grid-stiffened composite panels,” Composite Structures, 119, 767-776 (2015).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Azarafza.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 57, No. 2, pp. 261-290, March-April, 2021.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Davar, A., Azarafza, R., Fayez, M.S. et al. Dynamic Response of a Grid-Stiffened Composite Cylindrical Shell Reinforced with Carbon Nanotubes to a Radial Impulse Load. Mech Compos Mater 57, 181–204 (2021). https://doi.org/10.1007/s11029-021-09944-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-021-09944-3

Keywords

Navigation