Linear Vibrations of Nanotube-Reinforced Composite Conical Shell with Ring Stiffener

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DOI https://doi.org/10.15407/pmach2026.01.006
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. 29, no. 1, 2026 (March)
Pages 6-15
Cited by J. of Mech. Eng., 2026, vol. 29, no. 1, pp. 6-15

 

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

Iryna V. Biblik, Anatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine (2/10, Komunalnykiv str., Kharkiv, 61046, Ukraine), ORCID: 0000-0002-8650-1134

 

Abstract

Linear vibrations of thin-walled structure, which consists of nanotube-reinforced conical shell and ring stiffeners, are analyzed. Ring is attached at the end of truncated conical shell. Such shell structure describes adapter of rocket. Dynamic of such structure is actual problem of aerospace engineering. Material of this shell is nanocomposite, and ring is manufactured from isotropic material. Higher order shear deformation theory for the shell and Euler-Bernoulli theory for ring stiffeners are applied. The Rayleigh-Ritz method is used to derive the equations of the structure vibrations. The potential energy of the thin-walled structure is used. This potential energy consists of potential energy of the conical shell and potential energy of the ring. It is assumed that the ring vibrates in two perpendicular planes, performs vibrations in circumference directions, and torsional vibrations occur. The least action variational principle is used. As a result, the generalized eigenvalue problem is derived. The data of eigenfrequencies calculations is verified by finite element calculations in ANSYS software.

 

Keywords: functionally graded carbon nanotube-reinforced composite, truncated conical shell, parameters of linear vibrations.

 

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Received 02 February 2026
Accepted 03 March 2026
Published 30 March 2026