Double periodicity of mechanical properties of a thin ice field formed under conditions of lateral constraint

Abstract

Experimental data and results of theoretical modeling of the bending of a viscoelastic floating ice plate formed under constrained deformation are analyzed. When a thin plate of ice is frozen on the water surface under conditions of constrained deformation, which may be caused, for example, by the rigid walls of the pool, periodic changes in physical properties occur in it, in particular, periodic penetration resistance. Experimental results confirming this fact were obtained during tests of a thin ice cover at the Krylov State Research Center (Saint-Petersburg, Russia). A characteristic feature of the test results is that their spatial distributions can be represented with sufficient accuracy as an overlap of two periodic functions with significantly different periods: long-wave and short-wave components. In this paper, a detailed analysis of experimental data is given, which makes it possible to isolate these components. Furthermore, the theoretical model that explains the physical causes for double periodicity is proposed. The model assumes viscoelastic quasi-static deformation of the ice plate caused by small fluctuations of the water level in the basin and random disturbances of its surface. An analytical solution for the model case of cylindrical bending is derived. The solution is presented in the form of an expansion in terms of eigenfunctions of differential operators generated by the boundary value problem under study. It has been established that when a thin plate of ice freezes under conditions of constrained deformation, there are at least two reasons for the appearance of a periodic structure: a general loss of stability as an elastic structure and a local loss of stability by a viscoelastic-plastic mechanism. The results obtained can be used in the development of the theory of ice compression, in assessing the causes of variation in the local strength of ice fields and the possibility of their artificial destruction.

Keywords

• constrained deformation during freezing
• ice
• modal analysis
• plate
• resistance to through penetration
• viscoelastic