Nonlinear sloshing dynamics in rigid cylindrical shells under combined horizontal and vertical excitation

  • Elena Strelnikova orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine; Computer Physics and Energy Department, V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine; Applied Mathematics Department, Kharkiv National University of Radio Electronics, 61166 Kharkov, Ukraine
  • Andrii Rusanov orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine
  • Vasyl Gnitko orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine
  • Kyrylo Degtyariov orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine;  Computer Physics and Energy Department, V.N. Karazin Kharkiv National University, 61022 Kharkiv, Ukraine 
  • Denys Kriutchenko orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine
  • Andrii Kolodiazhnyi orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine
  • Demyd Sinchenko orcid

    A N. Pidhorny Institute of Power Machines and Systems, Ukrainian Academy of Sciences, 61023 Kharkov, Ukraine
Article ID: 4280
DOI: https://doi.org/10.59400/sv4280
Keywords: liquid-filled tanks, nonlinear sloshing, spectral boundary problem, singular integral equations, Rayleigh damping, resonance phenomena

Abstract

This paper presents the theoretical foundations for the nonlinear modelling of liquid sloshing dynamics in shells of revolution subjected to combined horizontal and vertical excitations. The proposed mathematical model integrates a spectral approach, the boundary element method (BEM), and a modal representation of the solution in generalized coordinates. This unified framework enables consistent analysis of both linear and nonlinear sloshing phenomena. The spectral boundary-value problem is reduced to a system of singular integral equations defined on the free and wetted surfaces of the shell. The 2π-periodicity of the integral operators is rigorously established, and the structure of the kernel singularities is identified. This ensures mathematical consistency and supports efficient numerical implementation. Natural sloshing modes and frequencies are computed using a BEM-based solver. Based on these eigenmodes, a modal expansion is constructed, leading to reduced-order systems of nonlinear ordinary differential equations. Governing equations are derived for both linear and nonlinear formulations, allowing detailed investigation of sloshing responses under simultaneous horizontal and vertical excitations. Rayleigh damping is incorporated into the modal system; its applicability and physical justification are discussed, along with its limitations in capturing energy dissipation in violent sloshing processes. Numerical results for rigid cylindrical shells illustrate the significant influence of nonlinear modal interactions and combined loading on free-surface elevation. The developed approach provides an effective tool for predicting complex sloshing behaviour beyond the capabilities of purely linear theory.

Published
2026-07-21
How to Cite
Strelnikova, E., Rusanov, A., Gnitko, V., Degtyariov, K., Kriutchenko, D., Kolodiazhnyi, A., & Sinchenko, D. (2026). Nonlinear sloshing dynamics in rigid cylindrical shells under combined horizontal and vertical excitation . Sound & Vibration, 60(4). https://doi.org/10.59400/sv4280
Issue
Vol. 60 No. 4 (2026)
Section
Article

Copyright (c) 2026 Elena Strelnikova, Andrii Rusanov, Vasyl Gnitko, Kyrylo Degtyariov, Denys Kriutchenko, Andrii Kolodiazhnyi, Demyd Sinchenko

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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