Full modeling of the mooring non-linearity in a two-dimensional floating structure

The dynamic behavior of a two-dimensional model of a small floating structure anchored by chains is analyzed. The structure is first modeled as a two-degrees-of-freedom oscillator with a strongly non-linear stiffness and subjected to a harmonic wave force. This type of structure is sometimes named Catenary Anchor Leg Mooring (CALM) system. The prescription of the vertical displacement leads to a simplified SDOF equation. An algebraic recurrence algorithm is employed to obtain a non-truncated differential equation that may be solved with the desired accuracy. Other authors have solved similar problems with approximate formulations of the geometric non-linearities. A numerical example is presented as an illustration. The time integration is carried out with a standard integration scheme and a power series approach. It is found that the response obtained after considering the strong non-linearity without previous truncations is qualitative different from the one found with a few terms of the expansions.