Kwok, Tsz Wai
(1989)
The calculation of second order forces acting on ships.
*University of Southampton, Doctoral Thesis*.

## Abstract

Linear strip theory is very useful in calculating the first order forces and moments for a ship in different modes of motion. However, linear strip theory cannot predict the higher order forces since the quadratic pressure term and the higher order wave potential term are assumed very small in comparison with the linear potential. This thesis is therefore to extend linear strip theory by including the higher order terms in order to find out the second order hydrodynamic force acting on a ship at different wave frequencies. The components of second order force consist of the quadratic pressure force, cross coupling force and second order wave potential force. The first two forces are obtained by the solution of linear theory. However, the second order potential force is more complicated because of the non-linear boundary conditions. Therefore the second order forces acting on a rigid body are calculated by using Green's theorem satisfying all boundary conditions. Frank Close Fit method is applied in calculating the first order radiative potential and its derivatives for a two dimensional section in heave motion. The second order pressure distribution on free surface is hence evaluated from the result of first order solution. The existence of `lq irregular frequencies in two dimensional source distribution calculation of the hydrodynamic coefficients is investigated. These irregular frequencies are removed by extending the source distribution onto the water line inside the cylinder and imposing a rigid wall boundary condition on that close water line. The second order time independent and time dependent forces for a two dimensional cylinder in heave motion are compared with the experimental measurements and published data. The comparisons show a satisfactory agreement between the theories and experiments. The program is then extended further to calculate the first and second order forces for a series 60 ship model. The first order hydrodynamic coefficients such as added mass and damping coefficients for this model are compared forces for this model at zero speed is also calculated. Finally, the higher order force and moment for two different types of vessels are investigated and the results show the non-linear characteristics between a tanker and a warship.

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