ABSTRACT

A numerical scheme is developed utilizing a Green's function and digital computer calculations to determine the excitation forces and moments as well as added mass and damping coefficients for floating bodies. The analysis is carried out within the framework of linear theory for bodies of arbitrary shape, either submerged or semi-submerged, in water of finite depth. The calculated hydrodynamic coefficients associated with both the wave excitation and response of the body are utilized in conjunction with the equations of motion in order to determine the response of a free-floating body to wave excitation. In addition, the steady-state drift force and uplift force are discussed for the case of free-floating and fixed bodies. Numerical results are presented for several configurations.

INTRODUCTION

The usual procedure for the placement of large concrete gravity structures involves construction in dry dock, floatation and towing of the structure to the deployment site followed by sink age through controlled ballasting. During the towing and sinking stages it is necessary to know the response of the structure to wave excitation. This is particularly true during sinking when the structure approaches and ventually sits on the bottom.

There is also another interesting feature of the floating body problem discussed herein. As waves interact with a floating structure, not only a periodic excitation force results, but in addition, the wave interaction results in a steady-state or time-independent horizontal force, vertical force and pitching moment. The steady-state horizontal force is usually referred to as drift force in ship hydrodynamics and generally causes an unrestrained floating body to drift in the direction of wave propagation. The time-independent uplift force may be important during the sinking of large structures since additional ballast beyond that needed for the calm water case must be provided for in order to sink the structure. This effect is particularly important in the case of structures which have small or no stabilizing waterline areas.

In the past the primary application of research relevant to the wave induced response of floating bodies has been in the area of surface ships. In view of the elongated shape of typical ships, a two-dimensional hydrodynamic analysis (strip theory) is generally employed. The assumption of infinite depth is also common to most of the published work in ship hydrodynamics. However, large ocean gravity structures are generally not constructed in the form of elongated bodies as in the case of ships and, therefore, strip theory is invalid, making a truly three-dimensional analysis of the fluid/structure necessary. Moreover, during the sinking operation the large object approaches and eventually rests on the ocean floor, and consequently, the bottom proximity or finite depth effect is also of interest. These features of the floating body problem have received little attention in the past by naval architects.

Several papers have treated the hydrodynamic coefficients for the two-dimensional problem associated with cylinders oscillating in water of infinite depth. Examples include those of Russell, Porter, Vogt?s, and Pauling and Richardson4 Equivalent data for three -dimensional shapes is much more limited, but Havelock5 has theoretically determined added mass and damping coefficients for a floating sphere, and ellipsoidal bodies oscillating on the free surface have been considered by Kim6. In a later paper Kim7 calculated the heave, surge, and pitch response for the same scherzo idol bodies to wave excitation. Barakat8 also treated the vertical motion of a sphere as induced