ST. PETERSBURG, March 16. /TASS/. Scientists at the Institute of Problems of Mechanical Engineering (the Russian Academy of Sciences) created a model to predict vibration conditions for structures operating in the Arctic ice conditions, such as oil platforms, and cut damage risks, the institute's press service told TASS.
"The model provides a theoretical basis for a more accurate assessment of forces affecting structures, depending on the ice speed, strength and on the mixture of water and ice properties in the fracture zone," the press service said. "Thus, the boundaries of dangerous modes may be predicted more accurately at the design stage. Knowing structure parameters and typical ice conditions in the installation area, engineers can use the model to assess whether the structure may be in a zone of resonance or chaos, and, if necessary, they may adjust the design to shift the danger zones beyond limits of realistically possible ice drift speed."
Engineering structures in the Arctic icy conditions are subject to the impact of moving ice fields that cause dangerous vibrations of structures. The structures' safety and durability depends directly on how accurately the structures' behavior may be predicted. Engineers distinguish three reactions of structures: intermittent ice crushing with moderate vibrations, resonant frequency capture (the most dangerous mode with a critical increase in amplitude) and continuous brittle crushing, characterized by complex, irregular behavior.
Existing models often have simplified the situation by considering ice as a monolithic medium, and water as only an additional mass attached to the structure. This approach did not take into account the important fact that water mixes up with ice in the contact area.
The institute's ex-Director, corresponding member of the Russian Academy of Sciences, Dmitry Indeitsev has come up with the idea to eye a two-phase medium, however his model considered only the first two modes of vibration. The institute's experts proposed to introduce into the model a more detailed description of the destruction zone - the space between the moving ice floe and the structure. In this zone, field observations show, ice not just presses the barrier - it crumbles, forming a complex two-phase mixture of water and ice fragments of different sizes.
"By taking into account this mixture's properties, its ability to accumulate or leave the gap, as well as the attention to random processes of ice pieces' breaking off and their sizes, we have managed to describe the three modes. This innovation has made it possible to explain how the same system may develop from a periodic reaction to resonance and then to chaotic behavior depending on the ice speed," the press service quoted Andrey Abrahamyan, chief researcher at the institute's Laboratory of Mathematical Modeling of Wave Processes, as saying.
How the model works
Having the model, scientist described all three classical modes of ice vibrations. Analytical results show that the transition from one regime to another is determined by competition between two factors: the time between ice impacts and the rate of energy dissipation. At low ice speeds, the fragments manage to leave the gap, and we can see steady periodic fluctuations of small amplitude.
As the speed increases to a critical level, conditions in the gap change so that the system enters resonance: the amplitude begins to rise sharply. Finally, at even higher speed, the interval between impacts becomes so short that the energy does not manage to dissipate. The system accumulates it, and this causes fluctuations disruption in a chaotic, broadband mode.