PSI - Issue 47

ScienceDirect Structural Integrity Procedia 00 (2022) 000 – 000 Structural Integrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Available online at www.sciencedirect.com ScienceDirect

www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia

Procedia Structural Integrity 47 (2023) 863–872

© 2023 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Abstract Based on the Donnell-Mushtari theory, procedures for determining conical shells' natural frequencies of vibrations with initial stress accounting are presented. To solve this problem first system of shell equations is transformed into ordinary differential equations using Fourier series decomposition, and then the obtained system is solved using ordinary polynomials. General dependencies which can be used for various boundary conditions, including elastic supports, are obtained. Also, an effort was made to account for initial stresses like axial force and pressure. The results are in good agreement with experimental and literature data. The given formulas are convenient to use in engineering applications, for example, to estimate the vibration frequency range of rocket and space engineering structures. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Keywords: conical shell, Transfer matrix method, Williams-Wittrick alghorithm, initial stress, elastic boundary conditions, dynamic analysis. 1. Introduction A cylindrical shell may be considered a special conical shell case when the side surface inclination angle equals zero. Therefore, by continuing the work Dubyk et al. (2018) on determining cylindrical shells' natural frequencies, it is possible to obtain a universal tool for modal analysis of such structures as airplane or rocket fairing, liquid tanks, submarine parts etc. The importance of a present study of the dynamics of the structure is confirmed by the events in Turkey-Syria 2023 where a large number of casualties were due to the destruction of buildings that could not withstand 27th International Conference on Fracture and Structural Integrity (IGF27) Free vibration of a conical shell with arbitrary boundary conditions using series solution Yaroslav Dubyk a *, Oleksii Ishchenko a,b , Mykola Kryshchuk b a LLC “IPP - Centre”, Kyiv 01013, Ukraine b NTUU «I. Sikorsky KPI», Kyiv 03056, Ukraine Abstract Based on the Donnell-Mushtari theory, procedures for determining conical shells' natural frequencies of vibrations with initial stress accounting are presented. To solve this problem first system of shell equations is transformed into ordinary differential equations using Fourier series decomposition, and then the obtained system is solved using ordinary polynomials. General dependencies which can be used for various boundary conditions, including elastic supports, are obtained. Also, an effort was made to account for initial stresses like axial force and pressure. The results are in good agreement with experimental and literature data. The given formulas are convenient to use in engineering applications, for example, to estimate the vibration frequency range of rocket and space engineering structures. © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons Keywords: conical shell, Transfer matrix method, Williams-Wittrick alghorithm, initial stress, elastic boundary conditions, dynamic analysis. 1. Introduction A cylindrical shell may be considered a special conical shell case when the side surface inclination angle equals zero. Therefore, by continuing the work Dubyk et al. (2018) on determining cylindrical shells' natural frequencies, it is possible to obtain a universal tool for modal analysis of such structures as airplane or rocket fairing, liquid tanks, submarine parts etc. The importance of a present study of the dynamics of the structure is confirmed by the events in Turkey-Syria 2023 where a large number of casualties were due to the destruction of buildings that could not withstand 27th International Conference on Fracture and Structural Integrity (IGF27) Free vibration of a conical shell with arbitrary boundary conditions using series solution Yaroslav Dubyk a *, Oleksii Ishchenko a,b , Mykola Kryshchuk b a LLC “IPP - Centre”, Kyiv 01013, Ukraine b NTUU «I. Sikorsky KPI», Kyiv 03056, Ukraine

* Corresponding author. Tel.: +38-044-502-45-70. E-mail address: dubyk-yr@ipp-centre.com.ua * Corresponding author. Tel.: +38-044-502-45-70. E-mail address: dubyk-yr@ipp-centre.com.ua

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons 2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons

2452-3216 © 2023 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the IGF27 chairpersons 10.1016/j.prostr.2023.07.100