Hydroelasticity is an emerging field of fluid-structure interaction with numerous applications in marine technology and Arctic engineering, particularly in relation to global warming and extreme weather phenomena. This multidisciplinary domain amalgamates fluid dynamics, structural mechanics, and wave propagation to examine intricate interactions among floating, submerged, and flexible structures. Recent improvements highlight the hydroelastic analysis of very large floating structures (VLFS) and floating ice sheets, which function as essential platforms for maritime space utilisation and as natural analogues in polar areas. Their dynamic behaviour under harsh climatic circumstances requires correct modelling in both homogeneous and stratified fluids, resulting in boundary value problems governed by Laplace or Helmholtz equations with higher-order, non–Sturm–Liouville type boundary conditions. Singularities at interfaces, resulting from discontinuities in material and fluid characteristics, exacerbate the dynamic response.

Significant focus has been placed on the phenomena of mode coalescence, multiple propagating modes, and blocking dynamics, wherein the convergence of modes at saddle or turning points modifies resonance characteristics and affects the conservation and redistribution of wave energy throughout the system. These effects are intricately associated with wave–wave interactions, affecting energy transfer, scattering, and attenuation processes in interconnected hydroelastic systems. Fourier analysis and related mathematical techniques offer robust frameworks for depicting intricate wave fields, addressing interface singularities, and scrutinising modal interactions with exceptional accuracy. This presentation provides a concise summary of recent advancements and the generalization of canonical analytical methods for modelling coupled hydroelastic systems, emphasizing their importance in understanding and designing VLFS, as well as studies on floating ice sheets in polar regions under extreme marine environments.