Linear Vibrations Analysis of a Composite Sandwich Conical Shell Manufactured by Additive Technologies

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DOI https://doi.org/10.15407/pmach2025.02.027
Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher Anatolii Pidhornyi Institute of Power Machines and Systems
of National Academy of Science of Ukraine
ISSN  2709-2984 (Print), 2709-2992 (Online)
Issue Vol. 28, no. 2, 2025 (June)
Pages 27-35
Cited by J. of Mech. Eng., 2025, vol. 28, no. 2, pp. 27-35

 

Authors

Kostiantyn V. Avramov, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), e-mail: kvavramov@gmail.com, ORCID: 0000-0002-8740-693X

Borys V. Uspenskyi, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), e-mail: Uspensky.kubes@gmail.com, ORCID: 0000-0001-6360-7430

Borys H. Liubarskyi, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova str., Kharkiv, 61002, Ukraine), ORCID: 0000-0002-2985-7345

Oleksii A. Smetskykh, National Technical University “Kharkiv Polytechnic Institute” (2, Kyrpychova str., Kharkiv, 61002, Ukraine), ORCID: 0009-0005-0238-9712

 

Abstract

The sandwich conical shell with elastic honeycomb structure, which is studied in this paper, is manufactured by additive technologies and has three layers. The honeycomb structure is made of ULTEM material, and the upper and lower face layers of the structures are made of carbon fiber. Each layer of the structures is an orthotropic material and satisfies Hooke’s law. Thanks to the homogenization procedure using the finite element method, we will obtain an equivalent orthotropic medium instead of the honeycomb structure. The elastic properties of this medium satisfy Hooke’s law. The modified high-order shear theory is used to model the deformation of the structures. The deformations of each layer of the structures are described by five variables, which include three projections of the displacements of the median surface and two angles of rotation of the normal to the median surface. To calculate the displacements of the layers, boundary conditions for stresses and boundary conditions that describe the continuity of displacements at the layers’ boundaries are used. The vibrations of a three-layer sandwich shell are expanded into basis functions that satisfy the kinematic boundary conditions. The Rayleigh-Ritz method is used to study the vibrations. The vibration parameters of structures are calculated from the eigenvalue problem. To verify the obtained results, the natural frequencies are compared with the data of finite element modeling. As follows from the calculations, the natural frequencies obtained by the Rayleigh-Ritz method and the finite element method are close. The spectrum of natural frequencies is very dense. The minimum natural frequency of vibrations is observed when the number of waves in the circular direction is equal to one.

 

Keywords: sandwich conical shell, honeycomb structure, linear vibrations.

 

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References

  1. Karimiasl, M. & Ebrahimi, F. (2019). Large amplitude vibration of viscoelastically damped multiscale composite doubly curved sandwich shell with flexible core and MR layers. Thin-Walled Structures, vol. 144, article 106128. https://doi.org/10.1016/j.tws.2019.04.020.
  2. Karimiasl, M., Ebrahimi, F., & Mahesh, V. (2019). Nonlinear forced vibration of smart multiscale sandwich composite doubly curved porous shell. Thin-Walled Structures, vol. 143, article 106152. https://doi.org/10.1016/j.tws.2019.04.044.
  3. Cong, P. H., Khanh, N. D., Khoa, N. D., & Duc, N. D. (2018). New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT. Composite Structures, vol. 185, pp. 455–465. https://doi.org/10.1016/j.compstruct.2017.11.047.
  4. Yadav, A., Amabili, M., Panda, S. K., Dey, T., & Kumar, R. (2021). Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory. Journal of Sound and Vibration, vol. 510, article 116283. https://doi.org/10.1016/j.jsv.2021.116283.
  5. Van Quyen, N., Van Thanh, N., Quan, T. Q., & Duc, N. D. (2021). Nonlinear forced vibration of sandwich cylindrical panel with negative Poisson’s ratio auxetic honeycombs core and CNTRC face sheets. Thin-Walled Structures, vol. 162, article 107571. https://doi.org/10.1016/j.tws.2021.107571.
  6. Zhang, Y. & Li, Y. (2019). Nonlinear dynamic analysis of a double curvature honeycomb sandwich shell with simply supported boundaries by the homotopy analysis method. Composite Structures, vol. 221, article 110884. https://doi.org/10.1016/j.compstruct.2019.04.056.
  7. Neigapula, V. S. N. & Sinha, P. K. (2007). Nonlinear free vibration analysis of laminated composite shells in hygrothermal environments. Composite Structures, vol. 77, pp. 475–483. https://doi.org/10.1016/j.compstruct.2005.08.002.
  8. Li, C., Shen, H.-S., Wang, H., & Yu, Z. (2020). Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core. International Journal of Mechanical Sciences, vol. 174, article 105472. https://doi.org/10.1016/j.ijmecsci.2020.105472.
  9. Li, Y., Li, F., & He, Y. (2011). Geometrically nonlinear forced vibrations of the symmetric rectangular honeycomb sandwich panels with completed clamped supported boundaries. Composite Structures, vol. 93, iss. 2, pp. 360–368. https://doi.org/10.1016/j.compstruct.2010.09.006.
  10. Reinaldo Goncalves, B., Jelovica, J., & Romanoff, J. (2016). A homogenization method for geometric nonlinear analysis of sandwich structures with initial imperfections. International Journal of Solids and Structures, vol. 87, pp. 194–205. https://doi.org/10.1016/j.ijsolstr.2016.02.009.
  11. Catapano, A. & Montemurro, M. (2014). A multi-scale approach for the optimum design of sandwich plates with honeycomb core. Part I: Homogenisation of core properties. Composite Structures, vol. 118, pp. 664–676. https://doi.org/10.1016/j.compstruct.2014.07.057.
  12. Amabili, M. (2018). Nonlinear mechanics of shells and plates in composite, soft and biological Materials. Cambridge: Cambridge University Press. https://doi.org/10.1017/9781316422892.

 

Received 11 December 2024

Accepted 15 January 2025

Published 30 June 2025