Analysis Of Barge Motion Using Strip And Three Dimensional Theories
Authors: Tligliore H.J. , Palo P.J. 
Published: October 2008

ABSTRACT
Strip theory is commonly used to analyze ship response to wave excitation for slender and shallow draft vessels. The two-dimensional nature of strip theory can introduce problems in analyzing barges, which have relatively low length-to-beam ratios and large draft. As part of recent OTEC work, three dimensional response theory has been developed into a computer model that can be applied to both slender and barge-like objects. The objectives of this study were to:utilize both of these theories to analyze, in a systematic manner, box-like shapes for various drafts, periods of excitation and length-to-beam ratios (LIB), andcompare results as calculated from each theory.
These results were for head-on seas only.
Comparisons are based on the response amplitude operators of heave, surge, and pitch as a function of LIB which ranged from 1.0 to 8.0. For the case of the pitch response operators at LIB = 8.0, shallow draft results were within 22% of each other; the deep-draft comparison was within 45%. Predicted response for heave showed less than 30% difference for both the shallow and deep draft floating boxes.
Results from the two theories were also compared to published experimental data from model tests. The objects analyzed were a 78 × 52 × 5-cm barge model, and a model of a 90 × 90 × 40-ffi floating box (1:100 scale). Again, only head-on seas were considered. The comparison shows that strip theory does not predict reliable results for these LIB ratios; the three dimensional theory, however, does agree very well with the model-responses reported.

INTRODUCTION
Navy requirements for predicting vessel motion are expanding into the areas of cable deployment and mooring. In particular, the Navy has been investigating systems for the placement of objects on the seafloor using cables, for deployment and construction of undersea cable structures, and for mooring of ships and buoys (Ref 2). For many of these cable operations the deployment (surface-supported) aspect is often the most critical from the standpoint of loads and changes in geometry (Ref 3). If the surface vessel is a ship or is ship-like in shape (i.e., relatively long and narrow), several theories (Ref 4) and associated computer programs (Refs 1,5,6) are available. However, for many ocean engineering operations, the support vessel is more barge-like in shape (i.e., short and wide). When applied to wide bodies the usual two dimensional solution procedures associated with the slender body assumption may lead to inaccuracies.

OBJECTIVES AND SCOPE
The objectives of this investigation were:Investigate the available theories for predicting large object motion response to wave excitation.Exercise these programs and compare results as given by two-dimensional strip theory and three-dimensional theory.Define the range of applicability of each theory, particularly in terms of length-to-beam ratio of the vessel.
For all cases considered in this study, waves were incident bow-on to the platforms; thus only heave, surge and pitch motions were computed. All platforms were assumed to be in deep water and to have a zero forward velocity.