Third and Higher Order Content of TLP Springing Excitation
Authors: Huse Erling , Stansberg Carl  Trygve 
Published: October 2008

SUMMARY
The present report describes an investigation quantifying to what extent the springing excitation on a tension leg platform can be fully described by quadratic wave forces, or whether third and/or higher order forces make a significant part of the excitation. The applied method of investigation consists in comparing experimentally measured excitation forces in irregular waves with corresponding forces obtained by a synthesis based cm the experimentally determined quadratic transfer functions.
The conclusions are that in low seastates (4 m significant wave height and less) the springing excitation on the TLP is dominated by quadratic forces. In higher seastates (8 m and more) only a small part of the excitation is of quadratic type.

1. INTRODUCTION
Tension leg platforms are normally designed to have their heave, roll, and pitch resonant frequencies well above the frequencies of the wave spectrum. This is in order to prevent first order wave forces from inducing excess ive resonant References and figures at end of paper. motions in these directions, which could lead to serious stresses in the tendons. However, due to non-linear wave forces there will be some excitation forces occurring at the frequencies above the frequency range of the wave spectrum. Thus there is still a possibility of significant fatigue stresses, and even contributions to the extreme loads in the tethers due to resonant heave, pitch, and roll. The phenomenon is often referred to as "springing" of the platform. The term springing is used to identify resonant responses which occur more or less continuously. Another term, "ringing", is used to identify peak resonant responses that occur only intermittently in steepand high single waves, and thus contribute to the extreme loads in the tendons. The terms "quadratic" or "second order" is used to denote non-linear wave force, proportional to the square of the wave elevation. "Third order" wave forces are proportional to the third power of the wave elevation, etc. Until now it has been customary to assume that springing excitation is mainly due to quadratic wave for-". It has been shown in previous reports (Refs.1 and 2) that present-day numerical methods based on potential flow theory predict the quadratic part of the wave excitation quite accurately. One question remains: Can third or higher order wave forces, or even more stochastic and unpredictable processes, such as vortex shedding or turbulence, contribute significantly to the springing excitation.

2. SCOPE OF PRESENT INVESTIGATION
In a previous report (Ref.1) the quadratic part of the wave forcing process has been measured andpresented in the usual form of QTFs (quadratic transfer functions). Fourier analysis of some regular wave tests in that report indicated significant contributions to the excitation in addition to the quadratic force. The objective of the investigations described in the present papers to quantify experimentally any third or higher order contributions to the springing excitation on a TLP in irregular waves.

3. MODEL DESCRIPTION
The experimental data were produced by testing of a 1:50 scale model of the SNORRE TLP hull. Fig.1 shows the main dimensions of the model.