Mathematical modelling of ice beam deflection dynamics

The assessment of stresses arising from the interaction of the ice field and inclined structures is an important part of research in ice mechanics. For these purposes, various mathematical tools are used, including mechanical models of beams. The article presents solutions for the equation of dynamic deflection of a beam with different boundary conditions, as well as taking into account the influence of a liquid located under the ice field. The inclusion of the base reaction in the beam deflection equation allows us to obtain an alternative model, which in some cases turns out to be more accurate than others. The obtained solutions are tested on the results of our own experiments conducted in an ice basin with model ice. In the experiments, the velocity of structures was varied; force projections, time, and place of the ice beam failure were recorded.