Stress-deformed state of a semi-infinite ice sheet under the action of a moving load

1994 ◽  
Vol 35 (5) ◽  
pp. 745-749 ◽  
Author(s):  
V. D. Zhestkaya ◽  
V. M. Kozin
Keyword(s):  
Moving Load ◽  
Ice Sheet ◽  
Deformed State

scholarly journals Dynamic Behavior of a Cylindrical Shell with a Liquid under the Action of Nonstationary Pressure Wave

TEM Journal ◽  
2021 ◽  
pp. 815-819
Author(s):  
Boris A. Antufev ◽  
Vasiliy N. Dobryanskiy ◽  
Olga V. Egorova ◽  
Eduard I. Starovoitov
Keyword(s):  
Cylindrical Shell ◽  
Galerkin Method ◽  
Pressure Wave ◽  
Moving Load ◽  
Algebraic Equations ◽  
Thin Cylindrical Shell ◽  
Incompressibility Condition ◽  
Nonlinear Algebraic Equations ◽  
Deformed State ◽  
The Galerkin Method

The problem of axisymmetric hydroelastic deformation of a thin cylindrical shell containing a liquid under the action of a moving load is approximately solved. It is reduced to the equation of bending of the shell and the condition of incompressibility of the liquid in the cylinder. The deflections of the shell and the level of lowering of the liquid are unknown. For solution, the Galerkin method is used and the problem is reduced to a system of nonlinear algebraic equations. A simpler solution is considered without taking into account the incompressibility condition. Here, in addition to the deformed state of the shell, the critical speeds of the moving load are determined analytically.

Nonlinear effects in the response of a floating ice plate to a moving load

2002 ◽  
Vol 460 ◽  
pp. 281-305 ◽  
Author(s):  
EMILIAN PĂRĂU ◽  
FREDERIC DIAS
Keyword(s):  
Shallow Water ◽  
Deep Water ◽  
Critical Speed ◽  
Moving Load ◽  
Ice Sheet ◽  
Phase Speed ◽  
Nonlinear Effects ◽  
Line Load ◽  
Weakly Nonlinear ◽  
Water Depths

The steady response of an infinite unbroken floating ice sheet to a moving load is considered. It is assumed that the ice sheet is supported below by water of finite uniform depth. For a concentrated line load, earlier studies based on the linearization of the problem have shown that there are two ‘critical’ load speeds near which the steady deflection is unbounded. These two speeds are the speed c0 of gravity waves on shallow water and the minimum phase speed cmin. Since deflections cannot become infinite as the load speed approaches a critical speed, Nevel (1970) suggested nonlinear effects, dissipation or inhomogeneity of the ice, as possible explanations. The present study is restricted to the effects of nonlinearity when the load speed is close to cmin. A weakly nonlinear analysis, based on dynamical systems theory and on normal forms, is performed. The difference between the critical speed cmin and the load speed U is taken as the bifurcation parameter. The resulting normal form reduces at leading order to a forced nonlinear Schrödinger equation, which can be integrated exactly. It is shown that the water depth plays a role in the effects of nonlinearity. For large enough water depths, ice deflections in the form of solitary waves exist for all speeds up to (and including) cmin. For small enough water depths, steady bounded deflections exist only for speeds up to U*, with U* < cmin. The weakly nonlinear results are validated by comparison with numerical results based on the full governing equations. The model is validated by comparison with experimental results in Antarctica (deep water) and in a lake in Japan (relatively shallow water). Finally, nonlinear effects are compared with dissipation effects. Our main conclusion is that nonlinear effects play a role in the response of a floating ice plate to a load moving at a speed slightly smaller than cmin. In deep water, they are a possible explanation for the persistence of bounded ice deflections for load speeds up to cmin. In shallow water, there seems to be an apparent contradiction, since bounded ice deflections have been observed for speeds up to cmin while the theoretical results predict bounded ice deflection only for speeds up to U* < cmin. But in practice the value of U* is so close to the value of cmin that it is difficult to distinguish between these two values.

Hydroelastic response of an ice sheet with a lead to a moving load

2021 ◽  
Vol 33 (3) ◽  
pp. 037109
Author(s):  
Y. Z. Xue ◽  
L. D. Zeng ◽  
B. Y. Ni ◽  
A. A. Korobkin ◽  
T. I. Khabakhpasheva
Keyword(s):  
Moving Load ◽  
Ice Sheet ◽  
Hydroelastic Response

Numerical Solution of Dynamic Responses of Moving Load on Ice Sheet

2011 ◽  
Vol 138-139 ◽  
pp. 44-49
Author(s):  
Ke Chen ◽  
Xue Feng Tong
Keyword(s):  
Differential Equation ◽  
Green Function ◽  
Moving Load ◽  
Ice Sheet ◽  
Hankel Transform ◽  
Peak Position ◽  
Dynamic Responses ◽  
Cylindrical Coordinate ◽  
Vibration Responses ◽  
Breaking Mechanism

To study on the breaking mechanism of an ice sheet under moving load, have need for researching the displacement responses of ice sheet. From viscoelastic vibration differential equation of ice sheet, dynamic equation of ice sheet was established under moving load in the cylindrical coordinate system, and the boundary conditions were given for solving differential equations. Used Hankel transform and Laplace transform to solve Green function of ice sheet vibration responses under loading, and derived the displacement response of ice sheet on the base of Green function. The example calculation shows that the displacement responses of ice sheet of 0.5m thickness is got under moving load at different time, the peak position of gravity wave propagation lags behind the loading point.

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