A method to compute the predicted wave responses of derrick vessels during heavy lift operation has been described. The general condition occurs when the lifted load is of comparable magnitude to the displacement of the vessel and hence, its effects cannot be ignored. Thus, the problem becomes an oscillating two-mass system and the interactions between the responses of the derrick vessel and the hanging load must be taken into account. A state-of-the-art approach of the linearized formulation of this physical problem is adopted. A solution to this problem and numerical examples, to demonstrate the effects for both displacement and semisubmersible type derrick vessels, are given.
It has been an industry standard for some time now to assume that during the lifting operation by a derrick vessel, the sea responses of the vessel can be predicted by considering the vessel itself i.e., the effects of the load can be neglected. This assumption was quite valid in the initial years of offshore construction business. But in the recent years, the advent of the heavy lift cranes and the giant derrick vessels (both displacement and semisubmersible hulls) has somewhat altered the picture. Because of the sheer size of these derrick vessels, it is quite common now to work in harsher sea conditions than it was ever possible before. And with the heavy lift cranes, it is entirely possible now to lift loads that constitute a significant fraction of the displacement of the derrick vessel Under these conditions it is no longer justified to use single (floating) body concept to determine derrick vessel sea responses. Rather, the concepts of oscillating two-body system with proper boundary conditions should be utilized. Here, one of the bodies is the derrick vessel itself and the other body being the lifted, hanging load. Also, proper connectivity conditions between these bodies are important. One should, then, solve for this entire physical system.
The vessel is assumed to be a rigid body with an Eulerian system of axes fixed on the vessel with origin at C coincident with the longitudinal center of gravity and X1,X2 are on still water surface as shown in Figure 1. The mathematical formulation is expressed in Cartesian tensor with implied summation convention. All variables with subscripts are assumed to be in the moving vessel fixed coordinate system, unless otherwise specified.
From Figure 1, it can be easily seen that the entire physical system of oscillating two-mass has 8 degrees of freedom. These are the conventional 6 degrees of freedom for a floating vessel and the additional 2 degrees (?1 and ?2) of freedom described by the swinging hosted load.
There are a number of ways to derive the equations of motion in these 8 degrees of freedom. These can be broadly categorized as Newton's and Lagrange's methods (Reference [1], [2].
