Three-Dimensional and Oblique Wave-Current Interaction with a Floating Elastic Plate Based on an Analytical Approach

An analytical hydroelastic model formulation in three-dimensional and oblique wave cases is developed to analyze the dynamic response of a horizontal, floating elastic plate subject to wave-current interaction under linearized small-amplitude wave theory. The floating elastic plate is moored to the bottom bed and free to the channel walls. Green’s function’s technique is utilised to determine the dispersion relation in 3D, and the series form of Green’s function in different water depths is derived in the oblique wave case. Further, the comparative analysis of phase and group velocities for different wave angles, between the present the existing models, is discussed. The derived dispersion relation is used in the solution by applying the geometrical symmetry velocity decomposition method. The present theoretical results of wave quantities are validated with the recently published and existing numerical hydroelastic model. A comparative analysis revealed a 1.7% difference between the present model and the existing hydroelastic models, and a 7.7% difference when compared to the model’s limiting cases. Several numerical results of the wave quantities, wave force, and vertical displacements are conducted to investigate the influence of current velocity on the hydroelastic response in three dimensions. It has been noted that the value of reflection coefficient diminishes for larger values of current velocity and the vertical displacement correspondingly becomes greater. This analysis will inform the design of elastic plate-based wave energy converters and breakwaters by clarifying how current loads affect the hydroelastic of a floating elastic plate with an oblique angle and three dimensions.