PSI - Issue 72

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ScienceDirect

Procedia Structural Integrity 72 (2025) 252–259

12th Annual Conference of Society for Structural Integrity and Life (DIVK12) Numerical analysis of natural frequencies of shallow shells under temperature load Alexander Kamenskikh a, *, Sergey Lekomtsev a , Valerii Matveenko a a Institute of Continuous Media Mechanics of the Ural Branch of the Russian Academy of Sciences, Academician Korolev Street, Perm 614013, Russian Federation Abstract The paper considers the natural vibration of a shallow cylindrical shell under temperature load. The use of equations of nonlinear elasticity theory in numerical calculations makes it possible to estimate the natural frequencies of the structure vibration due to temperature effect and after the loss of stability. The solution of the natural vibration problem for elastic body taking into account the preliminary stresses and strains is carried out based on the finite element method. The analysis of the obtained dependences allows us to conclude that after the buckling there is an increase in the lowest natural frequency of vibration and that the natural frequencies of shells with greater curvature is less sensitive to temperature load. © 2026 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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia

Keywords: Thermal loading; Shells; Buckling; Post-buckling; Nonlinear behavior; FEM

1. Introduction The design of structures operating in a wide temperature range poses the problem of evaluating not only temperature stresses, but also changes in the spectrum of natural frequencies of vibration, which can lead to undesirable vibration, noise, or even destruction of the structure due to resonance (Meyers and Hyer, 1991; Prabhu and Dhanaraj, 1994).

* Corresponding author. Tel.: +7-342-237-8330. E-mail address: kamenskikh.a@icmm.ru

2452-3216 © 2026 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 Aleksandar Sedmak, Branislav Djordjevic, Simon Sedmak Dr. Simon Sedmak, ssedmak@mas.bg.ac.rs, Innovation Center of Faculty of Mechanical Engineering, Belgrade, Serbia 10.1016/j.prostr.2025.08.100