scholarly journals Flexible plate and foundation modelling

2000 ◽  
Vol 4 (2) ◽  
pp. 103-110
Author(s):  
R. J. Hosking
Keyword(s):  
Critical Load ◽  
Gravity Waves ◽  
Velocity Potential ◽  
Moving Load ◽  
Phase Speed ◽  
Flexible Plate ◽  
Engineering Analysis ◽  
Flexural Gravity Waves ◽  
Railway Engineering ◽  
Engineering Parameters

In the most common mathematical model for a moving load on a continuously- supported flexible plate, the plate is assumed thin and elastic. An exception is the inclusion of viscoelasticity in the theory for the response of a floating ice plate, where the deflexion at the critical load speed corresponding to the minimum phase speed of hybrid flexural-gravity waves consequently approaches a steady state. This is in contrast to the elastic theory, where the response is predicted to grow continuously at this critical load speed. In the theory for a floating ice plate, the dominant pressure due to the underlying water is inertial, introduced via a velocity potential and the Bernoulli equation (assuming non-cavitation at the plate-water interface). On the other hand, the classical Winkler representation used in early railway engineering analysis corresponds to retaining a term which is generally negligible in the ice plate context. Critical load speeds are consequently predicted to be much higher, at wavelengths correspondingly much lower, for commonly accepted railway engineering parameters. Other models might be considered.

The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics

1978 ◽  
Vol 360 (1703) ◽  
pp. 471-488 ◽  
Keyword(s):  
Stream Function ◽  
Gravity Waves ◽  
Velocity Potential ◽  
Travelling Waves ◽  
Normal Modes ◽  
Phase Speed ◽  
Finite Amplitude ◽  
Fundamental Wave ◽  
Wave Steepness ◽  
Horizontal Scale

In this paper we embark on a calculation of all the normal-mode perturbations of nonlinear, irrotational gravity waves as a function of the wave steepness. The method is to use as coordinates the stream-function and velocity potential in the steady, unperturbed wave (seen in a reference frame moving with the phase speed) together with the time t. The dependent quantities are the cartesian displacements and the perturbed stream function at the free surface. To begin we investigate the ‘superharmonics’, i.e. those perturbations having the same horizontal scale as the fundamental wave, or less. When the steepness of the fundamental is small, the normal modes take the form of travelling waves superposed on the basic nonlinear wave. As the steepness increases the frequency of each perturbation tends generally to be diminished. At a steepness ak ≈ 0.436 it appears that the two lowest modes coalesce and an instability arises. There is evidence that this critical steepness corresponds precisely with the steepness at which the phase velocity is a maximum, considered as a function of ak. The calculations are facilitated by the discovery of some new identities between the coefficients in Stokes’s expansion for waves of finite amplitude.

scholarly journals Convergence of eigenfunction expansions for flexural gravity waves in infinite water depth

2021 ◽  
Vol 2070 (1) ◽  
pp. 012006
Author(s):  
Santanu Koley ◽  
Kottala Panduranga
Keyword(s):  
Gravity Waves ◽  
Water Depth ◽  
Water Waves ◽  
Eigenfunction Expansion ◽  
Velocity Potential ◽  
Wave Theory ◽  
Delta Function ◽  
Dirac Delta Function ◽  
Dirac Delta ◽  
Flexural Gravity Waves

Abstract In the present paper, point-wise convergence of the eigenfunction expansion to the velocity potential associated with the flexural gravity waves problem in water wave theory is established for infinite water depth case. To take into account the hydroelastic boundary condition at the free surface, a flexible membrane is assumed to float in water waves. In this context, firstly the eigenfunction expansion for the velocity potentials is obtained. Thereafter, an appropriate Green’s function is constructed for the associated boundary value problem. Using suitable properties of the Green’s functions, the vertical components of the eigenfunction expansion is written in terms of the Dirac delta function. Finally, using the property of the Dirac delta function, the convergence of the eigenfunction expansion to the velocity potential is shown.

scholarly journals Time-dependent response of a floating flexible plate to an impulsively started steadily moving load

1999 ◽  
Vol 381 ◽  
pp. 337-355 ◽  
Author(s):  
W. S. NUGROHO ◽  
K. WANG ◽  
R. J. HOSKING ◽  
F. MILINAZZO
Keyword(s):  
Steady State ◽  
Wave Speed ◽  
Moving Load ◽  
Phase Speed ◽  
Point Load ◽  
Time Dependent ◽  
Flexible Plate ◽  
State Response ◽  
Circular Load ◽  
Hybrid Waves

The time-dependent response of a floating flexible plate to an impulsively started steadily moving load defines the time taken to approach a steady-state deflection due to the load, or indeed whether such a steady state is achieved at all. The asymptotic analysis for large time reported here, for both a concentrated point load and a uniformly distributed circular load, confirms that a steady-state deflection is achieved at both subcritical and supercritical load speeds. This analysis also predicts a logarithmically growing response near the critical speed corresponding to the minimum phase speed of the hybrid waves generated, but an eventual steady-state response when the load speed moves at the shallow water wave speed. These results are supported by numerical computation.

scholarly journals Flexural-gravity waves in ice channel with a lead

2021 ◽  
Vol 921 ◽  
Author(s):  
L.D. Zeng ◽  
A.A. Korobkin ◽  
B.Y. Ni ◽  
Y.Z. Xue
Keyword(s):  
Gravity Waves ◽  
Flexural Gravity Waves

Abstract

Influence of snow cover on the parameters flexural-gravity waves in ice cover

2013 ◽  
Vol 54 (3) ◽  
pp. 458-464 ◽  
Author(s):  
V. M. Kozin ◽  
V. L. Zemlyak ◽  
V. Yu. Vereshchagin
Keyword(s):  
Snow Cover ◽  
Gravity Waves ◽  
Ice Cover ◽  
Flexural Gravity Waves

On resonant over-reflexion of internal gravity waves from a Helmholtz velocity profile

1979 ◽  
Vol 90 (1) ◽  
pp. 161-178 ◽  
Author(s):  
R. H. J. Grimshaw
Keyword(s):  
Velocity Profile ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Velocity Discontinuity ◽  
Interface Displacement ◽  
Boussinesq Fluid

A Helmholtz velocity profile with velocity discontinuity 2U is embedded in an infinite continuously stratified Boussinesq fluid with constant Brunt—Väisälä frequency N. Linear theory shows that this system can support resonant over-reflexion, i.e. the existence of neutral modes consisting of outgoing internal gravity waves, whenever the horizontal wavenumber is less than N/2½U. This paper examines the weakly nonlinear theory of these modes. An equation governing the evolution of the amplitude of the interface displacement is derived. The time scale for this evolution is α−2, where α is a measure of the magnitude of the interface displacement, which is excited by an incident wave of magnitude O(α3). It is shown that the mode which is symmetrical with respect to the interface (and has a horizontal phase speed equal to the mean of the basic velocity discontinuity) remains neutral, with a finite amplitude wave on the interface. However, the other modes, which are not symmetrical with respect to the interface, become unstable owing to the self-interaction of the primary mode with its second harmonic. The interface displacement develops a singularity in a finite time.

scholarly journals Measurements of sea-ice flexural stiffness by pressure characteristics of flexural-gravity waves

2013 ◽  
Vol 54 (64) ◽  
pp. 51-60 ◽  
Author(s):  
Aleksey Marchenko ◽  
Eugene Morozov ◽  
Sergey Muzylev
Keyword(s):  
Elastic Modulus ◽  
Gravity Waves ◽  
Water Depth ◽  
Water Pressure ◽  
Field Measurements ◽  
Effective Elastic Modulus ◽  
Flexural Stiffness ◽  
Flexural Gravity Waves ◽  
Using Data ◽  
Relative Errors

Abstract A method to estimate the flexural stiffness and effective elastic modulus of floating ice is described and analysed. The method is based on the analysis of water pressure records at two or three locations below the bottom of floating ice when flexural-gravity waves propagate through the ice. The relative errors in the calculations of the ice flexural stiffness and the water depth are analysed. The method is tested using data from field measurements in Tempelfjorden, Svalbard, where flexural-gravity waves were excited by an icefall at the front of the outflow glacier Tunabreen in February 2011.

scholarly journals Observation of Kelvin–Helmholtz instabilities and gravity waves in the summer mesopause above Andenes in Northern Norway

2018 ◽  
Vol 18 (9) ◽  
pp. 6721-6732 ◽  
Author(s):  
Gunter Stober ◽  
Svenja Sommer ◽  
Carsten Schult ◽  
Ralph Latteck ◽  
Jorge L. Chau
Keyword(s):  
Gravity Waves ◽  
Middle Atmosphere ◽  
Phase Speed ◽  
Velocity Measurements ◽  
Wind Variability ◽  
Short Period ◽  
Strong Shear ◽  
Summer Echoes ◽  
Period Wave ◽  
Horizontal Wavelength

Abstract. We present observations obtained with the Middle Atmosphere Alomar Radar System (MAARSY) to investigate short-period wave-like features using polar mesospheric summer echoes (PMSEs) as a tracer for the neutral dynamics. We conducted a multibeam experiment including 67 different beam directions during a 9-day campaign in June 2013. We identified two Kelvin–Helmholtz instability (KHI) events from the signal morphology of PMSE. The MAARSY observations are complemented by collocated meteor radar wind data to determine the mesoscale gravity wave activity and the vertical structure of the wind field above the PMSE. The KHIs occurred in a strong shear flow with Richardson numbers Ri < 0.25. In addition, we observed 15 wave-like events in our MAARSY multibeam observations applying a sophisticated decomposition of the radial velocity measurements using volume velocity processing. We retrieved the horizontal wavelength, intrinsic frequency, propagation direction, and phase speed from the horizontally resolved wind variability for 15 events. These events showed horizontal wavelengths between 20 and 40 km, vertical wavelengths between 5 and 10 km, and rather high intrinsic phase speeds between 45 and 85 m s−1 with intrinsic periods of 5–10 min.

scholarly journals Solitary flexural–gravity waves in three dimensions

2018 ◽  
Vol 376 (2129) ◽  
pp. 20170345 ◽  
Author(s):  
Olga Trichtchenko ◽  
Emilian I. Părău ◽  
Jean-Marc Vanden-Broeck ◽  
Paul Milewski
Keyword(s):  
Gravity Waves ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Boundary Integral ◽  
Three Dimensions ◽  
Cosserat Theory ◽  
Theme Issue ◽  
Flexural Gravity Waves ◽  
Forced Waves ◽  
Ice Phenomena

The focus of this work is on three-dimensional nonlinear flexural–gravity waves, propagating at the interface between a fluid and an ice sheet. The ice sheet is modelled using the special Cosserat theory of hyperelastic shells satisfying Kirchhoff's hypothesis, presented in (Plotnikov & Toland. 2011 Phil. Trans. R. Soc. A 369 , 2942–2956 ( doi:10.1098/rsta.2011.0104 )). The fluid is assumed inviscid and incompressible, and the flow irrotational. A numerical method based on boundary integral equation techniques is used to compute solitary waves and forced waves to Euler's equations. This article is part of the theme issue ‘Modelling of sea-ice phenomena’.

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