Oscillations of liquid in a vessel in the form of a rectangular parallelepiped

Stolbetsov, V. I.

doi:10.1007/bf01024800

Cited by 5 publications

(4 citation statements)

References 1 publication

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“…The literature contains only a few experimental and theoretical studies on the subject. Faltinsen et al [1][2][3] recognized a note by Stolbetsov,4 who was probably the first to study this problem theoretically. Arai et al 5,6 performed model tests and isolated Computational Fluid Dynamics ͑CFD͒ simulations.…”

Section: Introductionmentioning

confidence: 97%

Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

2006

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An adaptive asymptotic nonlinear modal system is used for systematic quantification of three-dimensional steady-state resonant sloshing in a square base tank with a finite fill depth. The depth/breadth ratios are ജ0.4. The tank is laterally excited with frequency close to the lowest natural frequency. The main emphasis is on the "swirling" wave regime and its special features, e.g., stability, feedback of higher modes, and regular and irregular switch of the apparent direction of rotation. Theoretical results are validated for both steady-state solutions and "beating" that does not die out in experimental investigations. Frequency domains with no stable steady-state waves and occurrence of "chaotic" waves are discussed.

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Section: Introductionmentioning

confidence: 97%

Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

2006

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“…(Abramson et al 1974 demonstrated this experimentally for a spherical LNG tank when the horizontal excitation amplitude is sufficiently large and the excitation amplitude is higher than the lowest natural frequency.) Stolbetsov (1967) may have been the first to study theoretically nonlinear resonant sloshing in a near-square basin due to horizontal harmonic forcing along one of the walls with excitation frequency close to the lowest natural frequency. He used the perturbation technique by Narimanov (1957) and postulated two types of steady-state solutions.…”

Section: Introductionmentioning

confidence: 99%

Resonant three-dimensional nonlinear sloshing in a square-base basin

2003

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An asymptotic modal system is derived for modelling nonlinear sloshing in a rectangular tank with similar width and breadth. The system couples nonlinearly nine modal functions describing the time evolution of the natural modes. Two primary modes are assumed to be dominant. The system is equivalent to the model by for the two-dimensional case. It is validated for resonant sloshing in a square-base basin. Emphasis is on finite fluid depth but the behaviour with decreasing depth to intermediate depths is also discussed. The tank is forced in surge/sway/roll/pitch with frequency close to the lowest degenerate natural frequency. The theoretical part concentrates on periodic solutions of the modal system (steady-state wave motions) for longitudinal (along the walls) and diagonal (in the vertical diagonal plane) excitations. Three types of solutions are established for each case: (i) 'planar'/'diagonal' resonant standing waves for longitudinal/diagonal forcing, (ii) 'swirling' waves moving along tank walls clockwise or counterclockwise and (iii) 'square'-like resonant standing wave coupling in-phase oscillations of both the lowest modes. The frequency domains for stable and unstable waves (i)-(iii), the contribution of higher modes and the influence of decreasing fluid depth are studied in detail. The zones where either unstable steady regimes exist or there are two or more stable periodic solutions with similar amplitudes are found. New experimental results are presented and show generally good agreement with theoretical data on effective domains of steady-state sloshing. Three-dimensional sloshing regimes demonstrate a significant contribution of higher modes in steady-state and transient flows.

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“…Stolbestov [15] theoretically studied the nonlinear sloshing regimes in almost-square base container under harmonic excitation along one of the base walls in vicinity of the sloshing lowest natural frequency. His approach was based on the perturbation method introduced by Narimanov [16] that assumed two steady-state sloshing regimes of planar waves and swirling wave.…”

Section: Introductionmentioning

confidence: 99%

Response regimes in equivalent mechanical model of moderately nonlinear liquid sloshing

Farid

Gendelman

2018

Nonlinear Dyn

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The paper considers non-stationary responses in reduced-order model (ROM) of partially liquid-filled tank under external forcing. The model involves one common degree of freedom for the tank and the non-sloshing portion of the liquid, and the other onefor the sloshing portion of the liquid. The coupling between these degrees of freedom is nonlinear, with the lowest-order potential dictated by symmetry considerations. Since the mass of the sloshing liquid in realistic conditions does not exceed 10% of the total mass of the system, the reduced-order model turns to be formally equivalent to well-studied oscillatory systems with nonlinear energy sinks (NES). Exploiting this analogy, and applying the methodology known from the studies of the systems with NES, we predict a multitude of possible nonstationary responses in the considered ROM. These responses conform, at least on the qualitative level, to the responses observed in experimental sloshing settings, multi-modal theoretical models and full-scale numeric simulations.

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Oscillations of liquid in a vessel in the form of a rectangular parallelepiped

Cited by 5 publications

References 1 publication

Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth

Resonant three-dimensional nonlinear sloshing in a square-base basin

Response regimes in equivalent mechanical model of moderately nonlinear liquid sloshing

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