Cnoidal Wave on a Long Elastic Floating Plate at Shallow Water Depth

This paper addresses the nonlinear waves propagating along a thin elastic plate floating in shallow water by using a numerical approach and by comparing with the analytical cnoidal wave theory. A numerical approach to simulate the nonlinear wave behavior on a floating plate is developed by incorporating the plate stiffness and inertia effects in the existing numerical method for free-surface waves. The accuracy and reliability of the newly developed numerical approach have been verified through comparisons with theoretical or experimental data from the literature. An analytical cnoidal wave solution for the propagation of cnoidal nonlinear waves along a floating plate is discussed and derived, too. This analytical approach aims to provide a foundational understanding of the complex wave dynamics exhibited by the floating plate. It turns out that the predictions from the analytical approach agree well with the numerical results in many cases while it still needs improvement.