Response of Jackup Models to Irregular Waves
Authors: Liu Ping , Massie W.W. , Wolters J.G. , Blaauwendraad J. 
Published: October 2008

ABSTRACT
This paper summarizes the laboratory studies of three principle jack-up models tested in irregular waves. The models tested can be categorized into two groups according to their nonlinear properties:Hydrodynamic drag with a nonlinear structure andRelative motion type.
The experimental data were analyzed in both the probability domain and frequency domain supported by a careful error analysis.
The test results and associated analyses demonstrate that: Different nonlinearities have different influences on the structure's dynamic behavior. Nonlinearity caused by relative motions manifests itself as damping. When drag and structural nonlinearities are of importance, the Response Amplitude Operator (RAO) shows a dependency on the input energy level as well as its energy distribution. Existence of drag results in a significant deformation in the probability distribution in such a way that the response becomes more extreme than the waves.
The results obtained from irregular waves also are compared with those obtained from regular waves. Additionally, the relative importance of various nonlinearities for the structural behavior are evaluated. Other phenomena such as signal filtering, etc, are also discussed.

INTRODUCTION
The primary objective of this work is to investigate the influence of hydrodynamic and P-? nonlinearities on elevated jack-up rigs. This work helps clarify the confusion existing in performance assessment of non-rigid slender structures where several nonlinearities are involved.
The detailed results and analysis concerning the regular wave tests have been given in earlier OTC paper [1].
Limited by space, only a small representative part of available results is included in this paper. More detailed presentations and interpretations are to be found in a separate report [2].
The present work forms a part of an on-going study of elevated jack-up durability carried out by the Workgroup of Offshore Technology of the Delft University of Technology. An overview of the progresses made so far in this program has been given in reference [3].

MODELS
Two principle physical models of three-legged jack-up structures - named Model I and Model II, respectively - were designed and fabricated. Additional testing of Model II with extra deck masses - then denoted as Model II-M - was carried out to expose the effects of deck load eccentricity the P-? effect and the effects of a variation in the natural period of the model.
These models each had three identical circular cylindrical legs; leg diameters were different for different models in order to accentuate the hydrodynamic drag and inertia effects. These were tested in the wave tank of the Ship Hydromechanics Laboratory of the Delft University of Technology.
Fig. 1 illustrates the physical model set-up. The most important parameters for each of the three models are listed in Table 1.
The analysis of the data obtained from the static tests and regular wave tests has shown that the model structures are highly nonlinear [1]. The nonlinearities originate from three sources: Structural - including imperfect deck to leg connection and P-? effect;Hydrodynamic - including wave kinematics, free surface effects and quadratic drag term; andRelative motion between waves and structure.