The paper highlights the differences between a time domain and a 2nd order frequency domain analysis of spar platforms using Morison's equation. Limitations of the frequency domain approach in representing the nonlinearities in forces and structural properties are shown. Monochromatic, bichromatic, trichromatic and irregular waves as well as current and wind loads are used for the parametric studies. In order to represent the nonlinear properties of the mooring lines in the frequency domain, the secant and tangent modulus are used when appropriate. Such combination of moduli is found to be more accurate than a ‘linearized’ representation of the structural properties.
Calculation of the structural response of a spar to the environmental loading encountered in deep oceans is a dynamic problem. The forces in the equations of motion are derived from modified Morison's equation or diffraction theory while the stiffness, mass and damping matrices are obtained from the concepts of structural dynamics. The equations describe the instantaneous structural response, so this is actually a time domain (t-d) problem. However, the solution in time domain is more expensive and provides little insight into the nature of the response. Moreover, in the problem formulation, some terms (e.g., radiation, added-mass) are frequency-dependent, and cannot be properly included in the time domain. If the frequency-dependence is significant, the frequency domain (f-d) solution is preferable. However, the latter only gives the steady-state response; therefore, to obtain the total responses, one has to convert the frequency domain results back to time domain and impose initial conditions. Further, the problem is only solved up to a certain order in the frequency domain. The system's nonlinearities are approximated in some manner, the most common approach being the ‘statistical linearization’. Obviously, these are only approximate models and their validity is not always satisfactory.
