Oil and gas exploration and production has been expanding in Arctic waters. However, numerical models for predicting the ice-induced vibrations (IIV) of offshore structures are still lacking in literature. This study aims to develop a mathematical reduced-order model for predicting the two-dimensional IIV of offshore structures with geometric coupling and nonlinearities. A cylindrical structure subject to a moving uniform ice sheet is analysed using the well-known Matlock model which, in the present study, is extended and modified to account for a new empirical nonlinear stress-strain rate relationship determining the maximum compressive stress of the ice. The model is further developed through the incorporation of ice temperature, brine content, air volume, grain size, ice thickness and ice wedge angle effects on the ice compressive strength. These allow the effect of multiple ice properties on the ice-structure interaction to be investigated. A further advancement is the inclusion of an equation allowing the length of failed ice at a point of failure to vary with time. A mixture of existing equations and newly proposed empirical relationships are used. Structural geometric nonlinearities are incorporated into the numerical model through the use of Duffing oscillators, a technique previously proposed in vortex-induced vibration studies. A one-degree-of-freedom (DOF) model is successfully validated against experimental results from the literature whilst the extended two-degree-of-freedom model produces new insights. Parametric studies highlight the effect of asymmetric geometric nonlinearities and ice velocity on the structural dynamic response. Results were compared to Palmer et al. (2010) which identified quasi-static, random-like or chaotic and locked-in motions. This numerical model has advanced the original Matlock model, showing a potential to be used in future IIV analysis of arctic cylindrical structures, particularly fixed offshore structures such as lighthouses, gravity bases and wind turbine monopiles.

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