PSI - Issue 81

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ScienceDirect

Procedia Structural Integrity 81 (2026) 434–438

VIII International Conference “In - service Damage of Materials: Diagnostics and Prediction“ (DMDP 2025) Determination of the natural oscillation frequencies of the pool tank with taking into account the hydrostatic pressure

Mykhailo Hud *, Denys Baran, Volodymyr Kaspruk Ternopil Ivan Puluj National Technical University, Ternopil, 46011, Ukraine

© 2026 The Authors. Copy from the contract: 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 DMDP 2025 organizers Keywords: natural frequencies; modal forms; pool; hydrostatic pressure; water mass; finite element modeling; dynamic behavior; reservoir structures; spatial vibrations; stiffness 1. Introduction The dynamic behaviour of liquid-containing reinforced concrete structures has been extensively studied due to its importance for assessing operational safety and vibration resistance. Foundational analytical models by Housner (1963) demonstrated that the presence of liquid significantly alters natural frequencies through added mass and hydrodynamic pressure effects. Veletsos and Yang (1977) later refined the theoretical framework for rectangular reservoirs, highlighting the strong dependence of modal behaviour on filling level and pressure distribution. These classical studies established the theoretical background for contemporary numerical investigations. Modern research increasingly adopts finite element methods (FEM), which allow accurate representation of material properties, spatial stiffness, and the depth-dependent hydrostatic pressure that governs the structural response of storage tanks. Kianoush and Ghaemmaghami (2011) showed that increasing water depth leads to substantial reductions in natural frequencies, Abstract The article presents the results of a numerical modal analysis of a reinforced concrete pool, taking into account hydrostatic pressure and water mass. The aim of this study was to determine the patterns of change in natural frequencies depending on the degree of filling of the pool. To perform calculations in the LIRA environment, a spatial model of the pool was constructed using volumetric finite elements. The study focused on three different states: a fully filled pool, a half-filled pool, and an empty pool. Analysis of the natural frequency spectra showed that in two cases – a fully and partially filled pool – the frequencies were in the high frequency range of 123 – 478 Hz. These frequencies showed a monotonous increase without sharp jumps, indicating high structural rigidity and uniform formation of more complex vibration modes. An empty pool is characterised by a significantly lower frequency range (87 – 338 Hz), indicating a decrease in rigidity and an increase in the sensitivity of the structure to dynamic influences. A comparison of the frequencies of the three states confirms that the presence of water contributes to an increase in the rigidity of the structure, while its absence shifts the spectrum to the lower part of the frequency range.

* Corresponding author. Tel.: +380-98-061-97-16. E-mail address: mishagud77@gmail.com

2452-3216 © 2026 The Authors. Copy from the contract: 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 DMDP 2025 organizers 10.1016/j.prostr.2026.03.075