Current Loads on a Horizontal Floating Flexible Membrane in a 3D Channel

Abstract

A 3D analytical model is formulated based on linearised small-amplitude wave theory to analyse the behaviour of a horizontal, flexible membrane subject to wave–current interaction. The membrane is connected to spring moorings for stability. Green’s function approach is used to obtain the dispersion relation and is utilised in the solution by applying the velocity decomposition method. On the other hand, a brief description of the experiment is presented. The accuracy level of the analytical results is checked by comparing the results of reflection and the transmission coefficients against experimental data sets. Several numerical results on the displacements of the membrane and the vertical forces are studied thoroughly to examine the impact of current loads, spring stiffness, membrane tension, modes of oscillations, and water depths. It is observed that as the value of the current speed (CS) rises, the deflection also increases, whereas it declines in deeper water. On the other hand, the spring stiffness has minimal effect on the vibrations of the flexible membrane. When vertical force is considered, higher oscillation modes increase the vertical loads on the membrane, and for a mid-range wavelength, the vertical wave loads on the membrane grow as the CS increases. Further, the influence of the phase and group velocities are presented. The influences of CS and comparisons between them in terms of water depth are presented and analysed. This analysis will inform the design of membrane-based wave energy converters and breakwaters by clarifying how current loads affect the dynamics of floating membranes at various water depths.

Keywords

• floating membrane
• spring mooring
• wave–current interaction
• analytical model
• phase and group velocity
• structural displacement