Title:

Effect of second order forces on steady tilt behaviours and some applications in dynamic positioning aspects of twin hulled marine vehicles

This thesis is in two volumes and the second one contains the Figures. Dynamic motion responses of twin hulled offshore structures, such as semi submersible drilling rigs, are of more concern to designers of offshore structures than those of ships, since it is not easy for such offshore structures to move away from stormy weather. These structures should operate stably around their fixed positions and, from the viewpoint of practical design and construction, they should be well designed to withstand severe wave excitation forces in general. A lot of the twin hulled offshore structures designed for developing the ocean resources are of two submerged long body configuration. Their behaviour in waves with crests parallel to the long bo4y axis are studied by considering the motion dynamics of two rigidly connected submerged cylinders in waves and the two dimensional radiation and diffraction problems are investigated with the forward speed effect (equivalent current effect). Under a linear assumption of the boundary value problem, the numerical solution is obtained exactly by solving the integral equation for the velocity potential on the body surface. Chapter One surveys the history of this research work on motion dynamics of floating offshore structures in waves. The new developing theories for predicting radiation forces and wave excitation forces to improve numerical accuracy and computational efficiency are reviewed and a preliminary study on the hydrodynamic behaviour of floating offshore structures in waves is performed. The practical prediction of the Froude Krylov forces acting on floating buoys and twin hulled vehicles in waves is also carried out. The engineering application of the hydrodynamic behaviour of the floating buoys with the mooring systems in waves is reviewed and extended to twin hulled offshore vehicles. In Chapter Two the complete boundary value problem is theoretically formulated for the velocity potential, which describes the unsteady flow around a submerged long cylinder advancing with a constant forward speed and with wave crests parallel to the long body axis. The theoretical terms due to the forward speed effect are included in the body boundary conditions. The effect of nonuniformity of the steady flow induced by the forward speed in the neighbourhood of the submerged structure is especially considered In Chapter Three the mathematical formulation of the Green function for this hydrodynamic problem is described theoretically and its derivatives are worked out for the solutions of the velocity potential over the body boundary contours in the integral equations. The mathematical manipulation of the Green function which makes the numerical computations more convenient is achieved. In Chapter Four comprehensive derivation of analytical expressions for the radiation and wave excitation forces acting on the submerged structure is described in detail. These forces are of first order with respect to the motion responses and wave amplitudes. Due to forward speed effect there is a contribution from the hydrodynamic restoring force terms proportion to the body displacement. The theoretical relation between the work done by the damping force and the energy transportation of the generated waves by the body motions is mathematically derived and is applied to confirm the accuracy of numerical computations. Based on such radiation forces and wave excitation forces, the motion equations of the dynamic responses of the submerged structure translating at a constant forward speed (equivalent current speed) in waves, but left to oscillate freely, are systematically formulated. In Chapter Five the theoretical formulation of the mvector contribution due to the effects of the forward speed and the interaction between two submerged hulls is derived by the image method. The mathematical expression of the mvector contribution for the single submerged circular or elliptical cylinder is also described. The predicted results in the hydrodynamic aspects with the mvector contribution are compared with and without taking the mvector contributions into consideration. The parametric studies are performed on the hydrodynamic characteristics such as the added mass and damping coefficients and the real and imaginary part of the Kochin functions, with and without the mvector contributions for different submerged depths, Froude number, separation distance and inclinations. In Chapter Six the mathematical formulation of the restoring forces due to the forward speed effect for the submerged single and twin circular cylinder cases is derived in detail and the numerical results of the submerged two circular cylinder case is confirmed by the analytical solution of the submerged single circular cylinder case. The dynamic motion responses of an inclined offshore twin hulled structure with and without restoring forces due to the forward speed effect in head and following waves are extensively investigated. The results of a parametric study of the dynamic motion responses of a twin hulled offshore structure for different submerged depths, Froude numbers (equivalent current effect), separation distances and inclinations in head and following waves are studied and discussed. Moreover, the dynamic motion behaviour of twin hulled marine vehicles in the low frequency region at resonance is also investigated.
