This article describes an investigation of the wave induced responses of constrained multiple bodies. The hydrodynamic analysis is based on linear diffraction theory, and the constraints in the connections between the bodies are imposed by the Lagrange multiplier technique. Results are given for two cases of two rectangular boxes connected by a hinge and by a rigid rod, which are compared with published data. An example of a tanker alongside a floating liquid natural gas (FLNG) barge is then considered, and the effect of the constraints on the responses is assessed.

Wave loading on marine structures is the major external force to be considered in the design of such structures. The accurate prediction of the nonlinear high-order components of the wave loading has been an unresolved challenging problem. In this paper, the nonlinear harmonic components of hydrodynamic forces on a bottom-mounted vertical cylinder are investigated experimentally. A large number of experiments were conducted in the Danish Hydraulic Institute shallow water wave basin on the cylinder, both on a flat bed and a sloping bed, as part of a European collaborative research project. High-quality data sets for focused wave groups have been collected for a wide range of wave conditions. The high-order harmonic force components are separated by applying the ‘phase-inversion’ method to the measured force time histories for a crest focused wave group and the same wave group inverted. This separation method is found to work well even for locally violent nearly-breaking waves formed from bidirectional wave pairs. It is also found that the $n$ th-harmonic force scales with the $n$ th power of the envelope of both the linear undisturbed free-surface elevation and the linear force component in both time variation and amplitude. This allows estimation of the higher-order harmonic shapes and time histories from knowledge of the linear component alone. The experiments also show that the harmonic structure of the wave loading on the cylinder is virtually unaltered by the introduction of a sloping bed, depending only on the local wave properties at the cylinder. Furthermore, our new experimental results reveal that for certain wave cases the linear loading is actually less than 40 % of the total wave loading and the high-order harmonics contribute more than 60 % of the loading. The significance of this striking new result is that it reveals the importance of high-order nonlinear wave loading on offshore structures and means that such loading should be considered in their design.