Non-stationary Response of a Carbon Nanotube-reinforced Composite Conical Shell

image_print
DOI https://doi.org/10.15407/pmach2020.02.021
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 23, no. 2, 2020 (June)
Pages 21-32
Cited by J. of Mech. Eng., 2020, vol. 23, no. 2, pp. 21-32

 

Authors

Kostiantyn V. Avramov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), e-mail: kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

Borys V. Uspenskyi, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), e-mail: Uspensky.kubes@gmail.com, ORCID: 0000-0001-6360-7430

Nataliia H. Sakhno, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), e-mail: natali.sahno@gmail.com, ORCID: 0000-0003-4179-5316

Iryna V. Biblik, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharskyi St., Kharkiv, 61046, Ukraine), e-mail: i.v.biblik@gmail.com, ORCID: 0000-0002-8650-1134

 

Abstract

This paper is devoted to the development of a method for the analysis of the non-stationary deformation of a carbon nanotube-reinforced composite shell under pulsed loading. The development of innovative manufacturing technologies has led to the emergence of new materials that have high potential for use in the aerospace industry. In particular, these include carbon nanotube-reinforced materials, or so-called nanocomposites. These materials demonstrate high strength and rigidity in combination with low weight, which is especially important when designing components of rocket and aircraft structures: fairings, fuel tanks, engines. At the same time, the behavior of structural elements under typical environmental influences requires additional studies due to the anisotropic and functional-gradient properties of materials. The determination of the mechanical properties of a nanocomposite is a known difficulty due to its anisotropic nature. There are various approaches to solving this problem. The simplest and at the same time well-proven one is the modified mixing rule, which is used in the paper. Equations of motion of the conical shell under the action of shock loading are obtained. To derive the equations of motion of the shell, a high-order theory is used that takes into account shifts and rotational inertia. To analyze the non-stationary dynamics of the shell, its free vibrations are analyzed. The analysis results are highly accurate compared to the finite element calculation carried out in the ANSYS software suite. A method is proposed for analyzing the dynamical response of the shell under the action of impact loading, which is based on the eigenvibration analysis of structures. Time dependencies of adapter deformations are obtained for the cases of actuation of two and four symmetrically arranged pyrodevices. The results of the analysis of the non-stationary dynamics of the adapter were compared with the finite element analysis results.

 

Keywords: conical shell, pulsed load, non-stationary process, nanocomposite material.

 

Full text: Download in PDF

 

References

  1. Seidel, G. D. & Lagoudas, D. C. (2006). Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mechanics of Materials, vol. 38, iss. 8–10, pp. 884–907. https://doi.org/10.1016/j.mechmat.2005.06.029.
  2. Liu, Y. J. & Chen, X. L. (2003). Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element. Mechanics of Materials, vol. 35, iss. 1–2, pp. 69–81. https://doi.org/10.1016/S0167-6636(02)00200-4.
  3. Odegard, G. M., Gates, T. S., Wise, K. E., Park, C., & Siochi, E. J. (2003). Constitutive modeling of nanotube–reinforced polymer composites. Composites Science and Technology, vol. 63, iss. 11, pp. 1671–1687. https://doi.org/10.1016/S0266-3538(03)00063-0.
  4. Allaoui, A., Bai, S., Cheng, H. M., & Bai, J. B. (2002). Mechanical and electrical properties of a MWNT/epoxy composite. Composites Science and Technology, vol. 62, iss. 15, pp. 1993–1998. https://doi.org/10.1016/S0266-3538(02)00129-X.
  5. Kanagaraj, S., Varanda, F. R., Zhil’tsova, T. V., Oliveira, M. S. A., & Simoes, J. A. O. (2007). Mechanical properties of high density polyethylene/carbon nanotube composites. Composites Science and Technology, vol. 67, iss. 15–16, pp. 3071–3077. https://doi.org/10.1016/j.compscitech.2007.04.024.
  6. Nejati, M., Asanjarani, A., Dimitri, R., Tornabene, F. (2017). Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes. International Journal of Mechanical Sciences, vol. 130, pp. 383–398. https://doi.org/10.1016/j.ijmecsci.2017.06.024.
  7. Hu, H., Onyebueke, L., & Abatan, A. (2010). Characterizing and modeling mechanical properties of nanocomposites. Review and evaluation. Journal of Minerals & Materials Characterization & Engineering, vol. 9, no. 4, pp. 275–319. https://doi.org/10.4236/jmmce.2010.94022.
  8. Mehrabadi, S. J. & Aragh, B. S. (2014). Stress analysis of functionally graded open cylindrical shell reinforced by agglomerated carbon nanotubes. Thin-Walled Structures, vol. 80, pp. 130–141. https://doi.org/10.1016/j.tws.2014.02.016.
  9. Zhang, L. W., Lei, Z. X., Liew, K. M., & Yu, J. L. (2014). Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels. Composite Structures, vol. 111, pp. 205–212. https://doi.org/10.1016/j.compstruct.2013.12.035.
  10. Song, Z. G., Zhang, L. W., & Liew, K. M. (2016). Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments. International Journal of Mechanical Sciences, vol. 115–116, pp. 339–347. https://doi.org/10.1016/j.ijmecsci.2016.06.020.
  11. Sobhaniaragh, B., Batra, R. C., Mansur, W. J., & Peters, F. C. (2017). Thermal response of ceramic matrix nanocomposite cylindrical shells using Eshelby-Mori-Tanaka homogenization scheme. Composites Part B: Engineering, vol. 118, pp. 41–53. https://doi.org/10.1016/j.compositesb.2017.02.032.
  12. Yaser, K., Rossana, D., & Francesco, T. (2018). Free vibration of FG-CNT reinforced composite skew cylindrical shells using the Chebyshev-Ritz formulation. Composites Part B: Engineering, vol. 147, pp. 169–177. https://doi.org/10.1016/j.compositesb.2018.04.028.
  13. Lei, Z. X., Liew, K. M., & Yu, J. L. (2013). Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment. Composite Structures, vol. 106, pp. 128–138. https://doi.org/10.1016/j.compstruct.2013.06.003.
  14. Lei, Z. X., Zhang, L. W., & Liew, K. M. (2015). Elastodynamic analysis of carbon nanotube-reinforced functionally graded plates. International Journal of Mechanical Sciences, vol. 99, pp. 208–217. https://doi.org/10.1016/j.ijmecsci.2015.05.014.
  15. García-Macías, E., Rodríguez-Tembleque, L., & Sáez, A. (2018). Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Composite Structures, vol. 186, pp. 123–138. https://doi.org/10.1016/j.compstruct.2017.11.076.
  16. Wang, Q., Cui, X., Qin, B., & Liang, Q. (2017). Vibration analysis of the functionally graded carbon nanotube reinforced composite shallow shells with arbitrary boundary conditions. Composite Structures, vol. 182, pp. 364–379. https://doi.org/10.1016/j.compstruct.2017.09.043.
  17. Wang, A., Chen, H., Hao, Y., & Zhang, Y. (2018). Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets. Results in Physics, vol. 9, pp. 550–559. https://doi.org/10.1016/j.rinp.2018.02.062.
  18. Moradi-Dastjerdi, R., Foroutan, M., & Pourasghar, A. (2013). Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method. Materials and Design, vol. 44, pp. 256–266. https://doi.org/10.1016/j.matdes.2012.07.069.
  19. Shen, H.-S. (2009). Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, vol. 91, iss. 1, pp. 9–19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  20. Wang, Q., Qin, B., Shi, D., & Liang, Q. (2017). A semi-analytical method for vibration analysis of functionally graded carbon nanotube reinforced composite doubly-curved panels and shells of revolution. Composite Structures, vol. 174, pp. 87–109. https://doi.org/10.1016/j.compstruct.2017.04.038.
  21. Reddy, J. N. (1984). A simple higher-order theory for laminated composite plates. ASME Journal of Applied Mechanics, vol. 51, iss. 4, pp. 745–752. https://doi.org/10.1115/1.3167719.
  22. Reddy, J. N. (1984). A refined nonlinear theory of plates with transverse shear deformation. International Journal of Solids and Structures, vol. 20, iss. 9–10, pp. 881–896. https://doi.org/10.1016/0020-7683(84)90056-8.
  23. Amabili, M. (2010). A new non-linear higher-order shear deformation theory for large-amplitude vibrations of laminated doubly curved shells. International Journal of Non-Linear Mechanics, vol. 45, iss. 4, pp. 409–418. https://doi.org/10.1016/j.ijnonlinmec.2009.12.013.
  24. Meirovitch, L. (1986). Elements of vibration analysis. New York: McGraw-Hill Publishing Company, 560 p.
  25. Avramov, K., Chernobryvko, M., Uspensky, B., Seitkazenova, K., & Myrzaliyev, D. (2019). Self-sustained vibrations of functionally graded carbon nanotubes reinforced composite cylindrical shell in supersonic flow. Nonlinear Dynamics, vol. 98, no. 3, pp. 1853–1876. https://doi.org/10.1007/s11071-019-05292-z.
  26. Chernobryvko, M. V., Avramov, K. V., Romanenko, V. N., Batutina, T. J., & Tonkonogenko, A. M. (2014). Free linear vibrations of thin axisymmetric parabolic shells. Meccanica, vol. 49, no. 8, pp. 2839–2845. https://doi.org/10.1007/s11012-014-0027-6.
  27. Gantmakher, F. R. (1966). Lektsii po analiticheskoy mekhanike [Lectures on analytical mechanics]. Moscow: Nauka, 300 p. (in Russian).

 

Received 30 April 2020

Published 30 June 2020