Session: 05-01-01 VLFS and New Concepts for Ocean Space Utilization

Paper Number: 127762

127762 - Cnoidal Wave on a Long Elastic Floating Plate at Shallow Water Depth 

Title: Cnoidal wave on a long elastic floating plate at shallow water depth 

Authors: Iijima, Soe, Maeda, Tatsumi

Key Words: Hydroelasticity, Nonlinear waves, shallow water, cnoidal wave, elastic plate

Very large floating structures (VLFS), floating solar panels, and ice sheets may be regarded as thin elastic floating plates. Analyzing the deformation of these structures under extreme wave conditions is crucial for ensuring safety, as failure could result in pollution, substantial costs, and potential loss of life. The interaction between fluid and structures causes nonlinear deformation waves to propagate along the floating plate, necessitating the development of nonlinear wave theories and nonlinear hydroelasticity theories. 

Despite the significance of studying nonlinear wave phenomena, research into waves traveling along thin elastic floating plates remains limited compared to the extensive work on linear waves. 

To date, some of the present authors have explored Stokes theory for waves traveling on a floating plate, discovering new insights through tank tests and analytical studies, primarily limited to deep waters. Considering the suitability of Stokes wave theory for intermediate and deep water, the cnoidal wave theory is proposed to identify the nonlinear response of floating plates in shallow waters. The newly developed cnoidal wave theory may also offer valuable insights into the behavior of these structures under Tsunami waves. 

This study aims to comprehensively understand the fundamental properties of the nonlinear wave that propagates along a thin elastic plate floating in shallow water, using the cnoidal wave theory. Both analytical and numerical approaches are pursued, with results cross-validated.

In this study, a cnoidal wave propagating on a floating plate in shallow water is presented analytically. Moreover, the existing numerical method for nonlinear free-surface waves proposed by Fenton in 1988 is utilized by incorporating the plate stiffness parameter EI, which can give a more accurate representation of the wave dynamics for floating plates. The accuracy and reliability of the newly developed numerical approach have been verified through comparisons with numerical/experimental data from literature.

Overall, the integration of plate stiffness into the cnoidal wave theory and the consideration of nonlinearity provide a comprehensive understanding of wave dynamics for floating plates in shallow water. The influence of stiffness in the context of cnoidal waves on a plate is particularly pronounced at high frequencies, according to the results of our parametric study. In contrast, the stiffness effect is relatively small, and both the free surface cnoidal wave and the cnoidal wave on the plate exhibit similar characteristics in low frequencies. However, it is worth noting that the nonlinearity of the waves is more prominent in shallow water, where the Ursell number is higher. The wave peaks along the floating plate become steeper, while the troughs become flatter due to the nonlinearity, which is particularly significant when a plate is installed in shallow water. 

On the contrary, it is remarkable that the nonlinearity found by the Cnoidal wave theory is different from that of Stokes’ wave theory for the waves propagating on the plate. In previous studies on Stokes’ wave propagating on the plate, the positive peak is higher than the negative peak as a result of nonlinearity in the low-frequency range while the negative peak is more prominent in the higher-frequency range and the nonlinearity was identified between the two frequency regimes where the wave response exhibited an unstable growth as an instability frequency while developing the second-order waves propagating along a floating plate in the analytical solution. These above findings contribute to the improvement of engineering designs and the safe operation of structures subjected to wave loads in shallow water environments.

 

 

 

 

Presenting Author: Soe Sandar Kyaw Osaka University

Presenting Author Biography: Soe Sandar Kyaw is a doctoral student at Naval Architecture and Ocean Engineering Department, Osaka University. She is a member of the Structural Integrity Subarea laboratory that focuses on ships and floating structures' responses and behavior. Her interest in Naval Architecture and Ocean Engineering started during her bachelor's study in Myanmar. Back then, she did her thesis “Study on Structural analysis of passenger ships running in the shallow water region of Myanmar”. Now, her study mainly focuses on nonlinear waves propagating along the floating structures.

Authors:

Kazuhiro Iijima Osaka University
Soe Sandar Kyaw Osaka University
Takeru Maeda Osaka University
Tatsumi Akira Osaka University