This paper presents frequency-domain hydroelastic analysis of a two-dimensional floating Structure in variable bathymetry by a hybrid technique based on Eigenfunction Matching Method (EMM), which has been validated by Tsai et al. (2011, 2014), in conjunction with Discrete Modules Method (DMM). The generalized incident wave field over an undulating seabed without the presence of floating structures is generated by use of EMM. The diffracted potential and radiated potential are obtained through the application of DMM and verified in a two-dimensional flat seabed problem since its previous applications were focused on three-dimensional wave-body hydroelastic interactions. The presence of a sloping seabed alters the common flat seabed condition, which causes wave reflection and shoaling, has a great influence on hydroelastic problems. Effects of seabed conditions, involving varying slope angle of the sloping seabed and varying relative positions between the floating structure and the sloping seabed, on hydroelastic responses of a floating structure are investigated by utilizing the proposed hybrid technique.


For floating structures, such as VLFS, which have large dimensions and relatively small structural rigidities, they have apparently flexible body responses rather than just rigid body movements in waves. Thus hydroelastic analysis are of great significance in design and safety assessment of this type of floating structures (Ding et al., 2017).

In the past several decades, development of hydroelasticity theory could be divided into four phases, i.e. 2D linear theory, 2D nonlinear theory, 3D linear theory and 3D nonlinear theory (Chen et al., 2006). Now, this theory has been widely employed to predict the motions, wave loads and sectional forces of elastic floaters in deep or shallow sea conditions. Water depth of most publications are assumed to be constant, which is practically valid when depth variation is small or in deep sea since the varying seabed topography has little effects on hydrodynamic responses of floaters in that cases. However, when the floating structure is deployed in complicated seabed environments such as islands or costal regions, hydroelastic responses of the floaters would be quite different from that in constant bathymetry. The main cause of the differences is that all waves including incident wave, diffracted wave and radiated wave would be scattered by the undulating sea bottom that would not occur in the flat seabed conditions, which has brought great challenges to hydroelastic analysis of floating bodies in environments of varying bathymetry. In this connection, many researchers have recently moved their focus to hydroelastic wave-body interactions over an realistic seabed. Athanassoulis and Belibassakis (1999) used the variational formulation and derived the consistent coupled-mode system(CCMS) to deal with linear wave propagation over a bed of arbitrary and consistent topography. By including a sloping-bottom mode, the Neumann condition on the sea bottom is satisfied. CCMS was extended by Belibassakis (2005) and applied to the hydroelastic analysis of large floating bodies of shallow draught lying over variable bathymetry regions. Kyoung et al. (2005) adopted finite element method based on the variational formulation in the fluid domain to calculate the sea-bottom effects. Song et al. (2005) employed the boundary element method (BEM) of the finite-water-depth Green function to investigate the hydrodynamic responses of a VLFS lying over uneven sea bottom and found that the effects of undulating seabed could not be neglected. Tian et al. (2014) proposed a new wave spectrum which assume that waves at different locations have different spectral forms, different wave direction angles and different but correlated phase angles to represent the non-uniform incident wave environment caused by complex seabeds near islands and reefs. Sources are distributed to represent the complex sea bottom and boundary element method is employed to calculate the diffraction potential and radiation potential in their work. A direct coupled method is established by Ding et al. (2017) to analyze the hydroelastic responses of floating bodies over undulating seabed. In their method, fluid domain is divided into inner region and outer region. Boussinesq equations and Rankine source method are employed to solve the wave propagation problem in the above-mentioned regions respectively. The continuity relations between the two regions are fulfilled through matching the wave elevation and distribution of velocity at the vertical interfaces. Wei et al. (2017) introduced a second fixed body on the seabed to represent the cylindrical bottom in diffraction theory and simulations can be accomplished with commercial codes like WAMIT. However, Buchner (2006) suggested that refraction and interference effects are too strong and affect wave exciting forces on the floaters in an incorrect way by using this method. In addition, a larger size of the the second body and smoother edges of this body do not improve the situation.

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