Approximate analytical solutions for pulse-induced displacement of floating ice on a slightly inclined seabed

This study develops a dynamic model for a viscoelastic ice floe over a gently sloping seabed, analyzing its transient response under impulsive loading via Hankel-Laplace transform. Model validity is confirmed against literature. Systematic analysis examines how seabed slope, water depth, ice thickness, and Young's modulus affect ice displacement. The Hankel transform proves superior to the Fourier transform for this problem class. Key findings: displacement amplitude increases with water depth but decays faster; larger slopes reduce amplitude and wavelength; thicker ice reduces amplitude with decay shifting from rapid to gradual; higher Young's modulus linearly reduces amplitude. In shallow water, wavelength shortening of flexural-gravity waves concentrates energy density, exponentially growing deflection amplitude. These results elucidate coupling among shallow-water effects, viscoelastic dissipation, and seabed topography, providing a theoretical basis for impulsive-load ice-breaking and for predicting dynamic ice response in polar engineering.