Nonlinear sloshing dynamics in rigid cylindrical shells under combined horizontal and vertical excitation - Strelnikova, Elena; Rusanov, Andrii; Gnitko, Vasyl; Degtyariov, Kyrylo; Kriutchenko, Denys; Kolodiazhnyi, Andrii; Sinchenko, Demyd (Sound & Vibration, 2026)
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.