Nonlinear Motion Response Of Floating Structures To Wave Excitation
Authors: Natvig Birger J. , Pendered John W. 
Published: October 2008

ABSTRACT
This paper describes the linearized and non-linear motion response of floating structures to regular waves. Special emphasism is laid on taut line moorings and linearized and non-linear response curves are shown for a version of the Aker Tethered Production Platform. The motion esponse of conventional semisubmersibles is also discussed and response curves for the Aker H3 are shown.
The linearized frequency domain method of analysis and the non-linear time history method are briefly discussed.
An approximate method for solving the nonlinear equations of motion based upon a Newton-Raphson type solution is proposed. This method, which is only valid for near linear systems, is shown to have practical applications for floating structures.

1. INTRODUCTION
This paper presents some of the results of a three year research project at Aker Engineering, in collaboration with the Department of Mechanical Engineering, University College London.
The tethered floating production platform the TPP - developed in recent years by the Aker Group is well known. Due to the high anchor stiffness, this structure will have different motion characteristics to that of the conventional semisubmersible. It was not apparent that the usual assumptions of linear motion could be applied to a tethered structure. The objective of the research was therefore to develop a computer based analysis of linearized and nonlinear motion response. The program to achieve this has two principal uses:Spectral analysis is the most common approach to dynamic studies of motion response yet it is dependent on the response being linear. A check on the linearity of the system is therefore desirable in order to justify this approach.The program can give the non-linear response for a given position in a given design wave and hence the instantaneous non-linear forces acting on each structural element can be calculated. These forces provide the input to a three dimensional structural space frame program, and the resultant element stresses are thus found.
This paper will only deal with the six rigid body degrees of .freedom, but the principles herein could also be extended to structure distortion coordinates.
Whilst the work on the tethered production platform provided the initial motivation for this project, the computer program will also handle semisubmersibles in a similar manner. The computer program named SEARESPONS is a module of the system SEACON which is currently being developed by Aker Engineering.
SEARESPONS was used for all dynamic analysis of the Aker TPP. This includes; motion response, mooring line design, loads for the structural analysis and offsets for marine riser design.

2. LINEARIZED ANALYSIS

2.1 Linear Forces
The first order (Airy) wave theory is implicit in linear analysis to calculate fluid particle accelerations and velocities and dynamic pressures. The corresponding wave forces are calculated by the well known Morison equation (see refs. 1,2,3) which is assumed to be valid as long as the cross-sectional dimensions are less than one fifth of the wave length.