Three-dimensional bent-gravity waves with non-uniform compression

Bukatov, A. E.; Zharkov, V. V.; Zav’yalov, D. D.

doi:10.1007/bf00850629

Cited by 9 publications

(2 citation statements)

References 5 publications

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“…We will consider the layer of an ideal incompressible heavy fluid of thickness H which occupies the domain , , , where x and y are the horizontal coordinates and z is the vertical coordinate directed upward. A thin elastic plate floating on the upper boundary of fluid can be described by the Kirchhoff-Love model with regard to the longitudinal, transverse and shear compressive forces [7,8]. Initially, the fluid and the plate are at rest but, starting from the instant t = 0, a time-dependent specified external pressure begins to act on the plate.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Three types of forces are possible in the three-dimensional case, namely, these are longitudinal, transverse and shear forces [5]. The behavior of free flexural-gravity waves in the presence of non-uniform compression was studied in [6] and the steady-state wave motion under the action of an external load was considered in [7]. The results of both studies were also given in monograph [8].…”

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confidence: 99%

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The Effect of Non-Uniform Compression of an Elastic Plate Floating on the Fluid Surface on the Development of Unsteady Flexural-Gravity Waves

Sturova

2021

Fluid Dyn

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The solution to the time-dependent 3D hydroelastic problem of vibrations of a thin elastic plate floating on the surface of a heavy fluid of finite depth under the action of unsteady external pressure is obtained within the framework of the linear formulation. The effect of the longitudinal, transverse, and shear compression of the plate on the development of flexural-gravity waves is studied. As examples, the periodic and pulse impact of a load is considered.

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Section: Formulation Of the Problemmentioning

confidence: 99%

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confidence: 99%

The Effect of Non-Uniform Compression of an Elastic Plate Floating on the Fluid Surface on the Development of Unsteady Flexural-Gravity Waves

Sturova

2021

Fluid Dyn

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Dynamical response of a floating ice sheet due to a forced oscillation in a running stream

Hossain,

2024

Physics of Fluids

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This paper explores the response of a floating ice sheet to a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite depth fluid. The floating ice sheet is modeled as a thin elastic plate following the Euler–Bernoulli beam equation, with the additional consideration of in-plane compressive forces acting on the ice. Employing linear wave theory, the problem is presented as an initial boundary value problem and is solved using Laplace and Fourier transforms to obtain a mathematical expression for the ice sheet's deflection in terms of infinite integrals. These integrals are thereafter solved asymptotically for large time and distance using the stationary phase method. The asymptotic analysis indicates a growing response over time when the poles and stationary points of the phase functions coalesce. The deflection of the floating ice sheet is graphically presented, highlighting the effects of various non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural gravity waves are derived from the dispersion relation and elucidated using diagrams. The results show that compressive force and current speed significantly influence wave amplitude, enhancing the oscillatory nature, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure have a substantial impact on the plate's deflection.

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Motion of a Load over an Ice Sheet with Non-Uniform Compression

Sturova

2021

Fluid Dyn

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Three-dimensional bent-gravity waves with non-uniform compression

Cited by 9 publications

References 5 publications

The Effect of Non-Uniform Compression of an Elastic Plate Floating on the Fluid Surface on the Development of Unsteady Flexural-Gravity Waves

The Effect of Non-Uniform Compression of an Elastic Plate Floating on the Fluid Surface on the Development of Unsteady Flexural-Gravity Waves

Dynamical response of a floating ice sheet due to a forced oscillation in a running stream

Motion of a Load over an Ice Sheet with Non-Uniform Compression

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