The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

Ping Wang

doi:10.1155/2015/308318

Abstract

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.

Highlights

In recent decades, there have been intensive researches on hydroelastic interaction between water waves and elastic plates in the area of ocean engineering and polar engineering in view of their academic research and applications
The very large floating structures (VLFSs), which are expected to serve as floating airports, artificial floating islands, ultralarge ships, or even mobile offshore bases, are mathematically assumed as elastic plates floating on a fluid for their strong flexibility and huge horizontal scales compared to vertical scales and characteristic wavelength
The hydroelastic deformation in the response of the structure to water waves is a predominant factor to design and maintain a safe and economic VLFS. Studies in this field were mainly focused on hydroelastic interaction between the water waves and the large ice sheets which were idealized as floating elastic plates [1], and the elastic plates are usually assumed to be semi-infinitely long in comparison with the wavelength of the incident wave [2, 3]

Summary

Introduction

There have been intensive researches on hydroelastic interaction between water waves and elastic plates in the area of ocean engineering and polar engineering in view of their academic research and applications. Studies in this field were mainly focused on hydroelastic interaction between the water waves and the large ice sheets which were idealized as floating elastic plates [1], and the elastic plates are usually assumed to be semi-infinitely long in comparison with the wavelength of the incident wave [2, 3]. We apply the homotopy analysis method (HAM) developed by Liao [14], a powerful analytic method for highly nonlinear problems, to consider the nonlinear hydroelastic response of a semi-infinite elastic plate floating on a fluid due to incident progressive waves. We investigate the dynamic influences of some important physical parameters, including incident wave amplitude, Young’s modulus, and the density and the thickness of the plate, on nonlinear hydroelastic response of the floating plate and the wave scattering

Mathematical Formulation

Analytical Approach Based on the HAM

Results and Discussion

Conclusions