Speaker: 王展研究员，中国科学院力学研究所

Inviter: 中国科学院数学院学术报告会组委

Title: From Ice Road to Duffing Oscillator: Resonantly Forced Hydroelastic Waves and Nonlinear Dynamics

Language: Chinese

Time & Venue: 2026.10.30 10:40-11:50 数学院南楼N204（数学院交流报告会）

Abstract: Floating ice sheets subject to moving loads experience complex hydroelastic responses of significant importance in polar engineering. In the ideal, inviscid framework, resonance near the minimum phase speed regularizes into solitary-wave structures, a mechanism echoing yet distinct from the upstream advancing solitons in classical surface gravity waves. However, such ideal models fail to capture the experimentally observed spatial symmetry breaking and downstream lag of maximum ice deflection. Incorporating linear dissipation bridges this gap, transforming the steady-state response into an S-shaped bifurcation structure marked by bistability and hysteretic transitions. To uncover the underlying dynamical essence, we systematically reduce the forced-dissipative Whitham equation onto a low-dimensional manifold, establishing a formal analogy to the forced-damped Duffing oscillator. This reduction reveals that the spatial lag between the load and the ice trough acts as a dynamic phase shift, which the system self-adjusts to satisfy a global power-balance condition. Consequently, the damping-to-load ratio emerges as the governing threshold for fold bifurcations, providing a robust predictive criterion for nonlinear jump phenomena in ice-sheet dynamics.