Two-dimensional problem of periodic loading of an elastic plate floating on the surface of an infinitely deep fluid

2005 ◽  
Vol 46 (3) ◽  
pp. 355-364 ◽  
Author(s):  
I. V. Sturova ◽  
A. A. Korobkin
Keyword(s):  
Elastic Plate ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Periodic Loading ◽  
Deep Fluid

scholarly journals The Response of a Poroelastic Ice Plate to an External Pressure

2021 ◽  
pp. 87-97
Author(s):  
Kristina N. Zavyalova ◽  
Konstantin A. Shishmarev ◽  
Alexander A. Korobkin
Keyword(s):  
Linear Theory ◽  
Elastic Plate ◽  
External Load ◽  
Oscillation Frequency ◽  
Hydrodynamic Pressure ◽  
Ice Cover ◽  
External Pressure ◽  
Two Dimensional ◽  
Liquid Penetration ◽  
Dimensional Problem

The response of a poroelastic ice cover to an external load is considered. The ice cover is modeled by a thin poroelastic floating plate within the linear theory of hydroelasticity. The porosity parameter is defined as the coefficient of proportionality of the velocity of liquid penetration into the plate and hydrodynamic pressure. The fluid under the plate is inviscid and incompressible. The flow caused by the ice deflection is potential. The external load is modeled by a localized smooth pressure. The two-dimensional problem of waves caused by a periodic external pressure on a floating porous-elastic plate is considered. The profiles of the generated waves are calculated for a given oscillation frequency of the amplitude of the external pressure. It was found that taking porosity into account leads to damping of oscillations in a distance from the external load

scholarly journals On waves in an elastic plate

1917 ◽  
Vol 93 (648) ◽  
pp. 114-128 ◽  
Keyword(s):  
Elastic Plate ◽  
Wave Length ◽  
Present Writer ◽  
Elastic Theory ◽  
Simple Problem ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Practical Solution ◽  
The Subject ◽  
Mathematical Difficulties

The theory of waves in an infinitely long cylindrical rod was discussed by Pochhammer in 1876 in a well-known paper. The somewhat simpler problem of two-dimensional waves in a solid bounded by parallel planes was considered by Lord Rayleigh and by the present writer‡ in 1889. The main object in these various investigations was to verify, or to ascertain small corrections to, the ordinary theory of the vibrations of thin rods or plates, and the wave-length was accordingly assumed in the end to be great in comparison with the thickness. It occurred to me some time ago that a further examination of the two-dimensional problem was desirable for more than one reason. In the first place, the number of cases in which the various types of vibration of a solid, none of whose dimensions is regarded as small, have been studied is so restricted that any addition to it would have some degree of interest, if merely as a contribution to elastic theory. Again, modern seismology has suggested various questions relating to waves and vibrations in an elastic stratum imagined as resting on matter of a different elasticity and density. These questions naturally present great mathematical difficulties, and it seemed unpromising to attempt any further discussion of them unless the comparatively simple problem which forms the subject of this paper should be found to admit of a practical solution. In itself it has, of course, no bearing on the questions referred to.

Modifications of the Godunov method for computing disturbance propagation in an elastic body

2016 ◽  
Vol 11 (1) ◽  
pp. 119-126 ◽  
Author(s):  
A.A. Aganin ◽  
N.A. Khismatullina
Keyword(s):  
Elastic Body ◽  
Godunov Method ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Order Accuracy ◽  
One Dimensional ◽  
Disturbance Propagation ◽  
Linear Waves ◽  
Longitudinal And Shear Waves ◽  
Contact Discontinuities

Numerical investigation of efficiency of UNO- and TVD-modifications of the Godunov method of the second order accuracy for computation of linear waves in an elastic body in comparison with the classical Godunov method is carried out. To this end, one-dimensional cylindrical Riemann problems are considered. It is shown that the both modifications are considerably more accurate in describing radially converging as well as diverging longitudinal and shear waves and contact discontinuities both in one- and two-dimensional problem statements. At that the UNO-modification is more preferable than the TVD-modification because exact implementation of the TVD property in the TVD-modification is reached at the expense of “cutting” solution extrema.

The Two-dimensional Problem with Free Boundary in Problems of Medicine

2021 ◽  
Author(s):  
Fatimat Kh. Kudayeva ◽  
Aslan Kh. Zhemukhov ◽  
Aslan L. Nagorov ◽  
Arslan A. Kaygermazov ◽  
Diana A. Khashkhozheva ◽  
...  
Keyword(s):  
Free Boundary ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Problem With Free Boundary

scholarly journals Inversion of Potential Vorticity Density

2017 ◽  
Vol 74 (3) ◽  
pp. 801-807 ◽  
Author(s):  
Joseph Egger ◽  
Klaus-Peter Hoinka ◽  
Thomas Spengler
Keyword(s):  
Boundary Conditions ◽  
Potential Vorticity ◽  
Potential Temperature ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Absolute Vorticity ◽  
Vertical Vector ◽  
The North ◽  
And Function

Abstract Inversion of potential vorticity density with absolute vorticity and function η is explored in η coordinates. This density is shown to be the component of absolute vorticity associated with the vertical vector of the covariant basis of η coordinates. This implies that inversion of in η coordinates is a two-dimensional problem in hydrostatic flow. Examples of inversions are presented for (θ is potential temperature) and (p is pressure) with satisfactory results for domains covering the North Pole. The role of the boundary conditions is investigated and piecewise inversions are performed as well. The results shed new light on the interpretation of potential vorticity inversions.

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