This paper describes a methodology to perform the dynamic analysis, in the frequency domain, of fixed or compliant offshore structures. The method permits the calculation of the main part of the non linear hydrodynamic forces using a second order spectral approach under the form of convolution product of wave kinematics spectra. Then, the dynamic response includes both the linear part related with the wave and wind spectra and the main part of non linear drift forces in low and high frequency ranges.

A comparison with a time domain analysis is presented. This comparison shows good accordance between the complete non linear analysis performed in the time domain and the frequency domain calculation.


The design of jackets and compliant structures for deep waters is mainly governed by dynamic and fatigue criteria.

A precise determination of the dynamic response of these structures to environmental conditions is then of major importance.

Two ways can be used to perform such analysis. The first one consists in determining the time histories of nodal displacements and member stresses; a statistical analysis of the time series gives informations about expected mean and extreme values of the critical parameters for the design.

The second method of analysis consists in a frequency domain analysis, for which, the determination of a set of transfer functions makes it possible to compute the dynamic response of the structure under the form of response spectra.

Both methods present advantages and drawbacks. The time domain analysis makes it possible to take into account any type of non linear forces, as drag forces or drift due to water level fluctuations but this analysis requires a lot of computer time specially for large structures of several hundred nodes.

The frequency domain approach is cheaper but requires usually the linearization of the non linear terms of the equations of motion.

This linearization seems non acceptable for compliant structures for which the drift forces due to water level fluctuations in random seas can induce significant motions and stresses at low and high frequencies, far away from the range of the dominant wave frequencies.

In order to obtain, in the frequency domain, a sufficiently good description of the dynamic response of a structure in random seas, a second order spectral analysis has been used. This analysis gives a good approximation of non linear drift force spectra. This relatively new method has been applied and compared with a time domain analysis as explained hereafter. To do this, three computer programs have been used.

These two dynamic analysis methods, in the frequency domain and in the time domain, have been used for the design of the Gamma Tower, a compliant structure for deep water. The comparison between the results obtained in both cases has shown very good accordance between the two methods. It is worth noting that this comparison is particularly interesting since the drag component, which induces the non linearities, is relatively large and corresponds, in the upper part of the Gamma Tower, to a classical jacket- type structure.

This content is only available via PDF.
You can access this article if you purchase or spend a download.