Modeling dynamic ice–structure interaction with failure zones: Predicting resonance and chaotic responses

This paper develops a new analytical and numerical framework to study the nonlinear dynamics of elastic structures under intermittent, shock-like loading from drifting ice floes. Unlike conventional models, we take into account a mixture of water and ice in a failure zone at the ice–structure interface that allows us to describe complex behavior including periodic, resonant, and chaotic regimes. Using a Poincaré map approach, we derive asymptotic expressions for oscillation amplitudes and identify resonance conditions. Near resonance, oscillations amplify significantly, with sensitivity to damping and failure-zone properties. Random pulse loading is modeled via iterated function systems (IFS), predicting fractal attractors under weak damping. Simulations confirm these patterns and match experimental trends linking amplitude to ice velocity. The model captures three key regimes — periodic motion, resonance amplification, and chaotic response — and offers insight into how failure zones affect structural dynamics in ice-covered polar marine environments, supporting better prediction and mitigation of ice-induced vibrations.