Keywords: non-linear, spectral analysis, offshore platforms, finite elements.

The author has developed a novel non-linear spectral model (NONLIN) [1] for modelling lattice structures in two dimensions. The model uses the finite element method to construct the equations of motion of the system and uses the convolution integral to include higher order harmonic responses due to the non-linear drag force term in Morrison's equation.

Details are presented of a non-linear spectral model using a perturbation technique. In this development some of the non-linear dependencies of excitation on wave kinematics through the drag force term are maintained; linear Airy wave theory is used to describe the wave kinematics. The methodology is based on the modified Morison equation [1], incorporating the effects of relative velocities and accelerations and the hydrodynamic damping terms are time varying.

In particular, this development is an extension of research carried out by Lipsett [2] and Eatock-Taylor and Rajagopalan [3] who considered the effects of non-linearities on single degree of freedom systems and lumped mass systems respectively. The non-linear model described herein has been developed to model structures in two dimensions and is used to investigate the effects of leg spacing on spectral response due to the higher order harmonics in the force term.

Since the non-linear response utilises the third-order convolutions of water particle velocity spectra, it is instructive to consider the third-order convolution of a velocity spectrum to see the effect of this non-linearity on the force spectrum. The effect of depth attenuation on velocity convolutions is considered and presented; also, in the paper the non-linear spectra of forces computed by NONLIN are compared with linear spectra and with non-linear spectra from the literature.

From their research Eatock-Taylor and Rajagopalan [3] concluded that 'The influence of the non-linearities has been demonstrated to be smaller at lower sea-states'. For the structures considered, the current research shows that when leg spacing is included in the analysis then the discrepancies between the linear and non-linear response spectra are greatest at lower sea-states. This is an important conclusion because lower sea-states have a higher frequency of occurrence and thus the fatigue life of structural members may be affected.

Eatock-Taylor and Rajagopalan [3] also concluded that the difference between the linear and non-linear response spectra '... is negligible around the frequencies of maximum wave energy, but significant at resonance'. The analysis carried out in this research on a cantilever leads to similar conclusions. However, this is not the situation when analysing portal frames; in this situation the main difference occurs close to the frequencies of maximum wave energy due to the higher order effects interacting with the leg spacing phase effects.

1

Hartnett, M., "An Analysis of the Effects of Leg Spacing on Spectral Response of Offshore Structures", Journal of Advances in Engineering Software, 31, 991-998, 2000 doi:10.1016/S0965-9978(00)00065-X

2

Lipsett, A.W., Nonlinear Response of Structures in Regular and Random Waves, Ph.D. Thesis, Department of Civil Engineering, The University of British Columbia, Canada, 1985

3

Eatock-Taylor, R. and Rajagopalan, A., "Dynamics of Offshore Structures, Part I: Perturbation Analysis", Journal of Sound and Vibration, 83(3), 410-416, 1982

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