The force effects due to wave action on offshore structures are conventionally determined using Morison's equation. This is a nonlinear relation in velocity, conventionally represented by an equivalent linearisation for converting wave velocities to forces, necessary to allow structural dynamic analysis by frequency domain methods (the most commonly applied approach). The suggested approaches for the linearisation can be shown to be of essentially two classes; those equivalent to Borgman's approach and those equivalent to Bolotin's. In general, it is not clear, a priori, which is more the appropriate. Nor is it clear whether these classical linearisations are relevant, particularly when structural fatigue is to be estimated (e.g., through the Palmgren-Miner rule). A criterion for derivation of a linearisation constant under fatigue considerations can be derived relatively simply. Unfortunately the criterion is not easily applied except by iteration. A sensitivity study has been performed for a simple but realistic offshore structure to estimate the relative importance of correctly estimating the linearisation constant.
In the analysis of offshore structures, it is conventional to use Morison's equation to describe the force per unit length, p(t), normal to a tubular member, as a function of the water particle velocity u(t) and the water particle acceleration út In equation (1) the drag coefficient Cd and the mass coefficient Cm are each known to be subject to considerable uncertainty (e.g., Sarpkaya and Isaacson, 1981). The equation is also non-linear in water particle velocity u(t). This is of no particular significance when time. domain methods for structural analysis under time dependent loadIng are used. However, frequency domain (Le., spectral) methods are more commonly employed and for these it is necessary to assume:
that all random variables are described by the normal distribution; and
that there are linear transformations between spectral descriptions.
The non-linear drag term in equation (1) is, therefore,
