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

The combined motion of a rigid cylindrical tank filled with a fluid with a free surface and a moving platform attached to the tank by a spring is simulated mathematically. The nonlinear oscillations of this system caused by a harmonic force applied to the platform are studied Keywords: rigid cylindrical tank, fluid with free surface, moving platform, nonlinear oscillations, variational algorithmIntroduction. The technological advancement motivates solving the dynamic problem for structures partially filled with a fluid and subjected to different boundary conditions. Fluid-filled tanks on a moving platform are used as components of engineering structures in mechanical engineering, rocket technology, aircraft construction, fluid carriers and storages [1,13,14]. Various aspects of the behavior of such systems without elastic elements were addressed in [3-9, 13, 14, 16-20]. The influence of the elastic properties of structures contacting with a fluid are studied in [10-12, 15, 21] with, however, little attention given to the motion of a fluid with free surface. Mathematically, such problems are described by inhomogeneous equations (a coupled nonlinear system of ordinary differential equations and a nonlinear boundary-value problem with free boundary). The analytic solutions of such nonstationary nonlinear boundary-value problems have not yet been found. Therefore, approximate methods mainly based on variational algorithms and methods of nonlinear mechanics are used. Here we study the nonlinear coupled oscillations of a perfectly rigid cylindrical tank partially filled with a fluid and attached by a spring to a platform exerting harmonic loading on the tank.1. Problem Formulation. Subject of Analysis. Consider a perfectly rigid cylindrical tank partially filled with a fluid and attached by a spring to a platform moving over a horizontal plane. The platform-tank-fluid system is initially at rest. A harmonic force F A t = cos( ) w (w = 3.8, 4.0, 4.14, 4.3, 5.2, A = 662 N) is applied to the platform. A general view of this

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“…Mathematical modeling reveals that the oscillations do not stabilize in all modes, and this is confirmed by recent experiments [6,16].…”

Section: Mathematical Model Of the Mechanical Systemsupporting

confidence: 71%

Influence of Spring Attachment on the Dynamics of a Fluid-Filled Cylindrical Tank on a Moving Platform

Limarchenko

Tkachenko

2014

Int Appl Mech

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“…Complications in measuring the amplitude responses for 'swirling' are caused by the occurrence of breaking waves. See, for details [56] and, for 'swirling' in a square-base tank, [57].…”

Section: Validation By Experimentsmentioning

confidence: 99%

Sloshing in a vertical circular cylindrical tank with an annular baffle. Part 2. Nonlinear resonant waves

Gavrilyuk¹,

Lukovsky

Trotsenko

et al. 2006

J Eng Math

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Weakly nonlinear resonant sloshing in a circular cylindrical baffled tank with a fairly deep fluid depth (depth/radius ratio ≥ 1) is examined by using an asymptotic modal method, which is based on the Moiseev asymptotic ordering. The method generates a nonlinear asymptotic modal system coupling the time-dependent displacements of the linear natural modes. Emphasis is placed on quantifying the effective frequency domains of the steady-state resonant waves occurring due to lateral harmonic excitations, versus the size and the location of the baffle. The forthcoming Part 3 will focus on the vorticity stress at the sharp baffle edge and related generalisations of the present nonlinear modal system.

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“…Horizontally excited waves have received less attention and workers have concentrated on the case of containers with a modérate width (Miles 1984;Funakoshi & Inoue 1988;Nobili et al 1988;Feng 1997;Billingham 2002;Hill 2003;Faltinsen, Rognebakke & Timokha 2006), whose horizontal size is comparable to the surface waves wavelength. In this case, only a few (depending on symmetries) sloshing modes are excited; note that depth plays no role in this discussion, and only affects the eigenmodes quantitatively.…”

Section: Introductionmentioning

confidence: 99%

Modulated surface waves in large-aspect-ratio horizontally vibrated containers

Varas

Vega

2007

J. Fluid Mech.

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We consider the harmonio and subharmonic modulated surface waves that appear upon horizontal vibration along the surface of the liquid in a two-dimensional large-aspect-ratio (length large compared to depth) container, whose depth is large compared to the wavelength of the surface waves. The analysis requires us also to consider an oscillatory bulk flow and a viscous mean flow. A weakly nonlinear description of the harmonic waves is made which provides the threshold forcing amplitude to trigger harmonic instabilities, which are of various qualitatively different kinds. A linear analysis provides the threshold amplitude for the appearance of subharmonic waves through a subharmonic instability. The results obtained are used to make several specific qualitative and quantitative predictions.

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

Cited by 71 publications

References 28 publications

Influence of Spring Attachment on the Dynamics of a Fluid-Filled Cylindrical Tank on a Moving Platform

Influence of Spring Attachment on the Dynamics of a Fluid-Filled Cylindrical Tank on a Moving Platform

Sloshing in a vertical circular cylindrical tank with an annular baffle. Part 2. Nonlinear resonant waves

Modulated surface waves in large-aspect-ratio horizontally vibrated containers

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