Within the frame of potential theory and the assumption of weak nonlinearity of wave motion, a numerical method is developed for the third order triple-frequency wave loads on fixed axisymmetric bodies in monochromatic incident waves. Applying the numerical code, numerical computations were carried out for surge and heave forces and pitch moments on a uniform cylinder, truncated cylinders and a hemisphere. Examinations were made on the contribution to third order forces and moments from potentials at each wave orders, and the relation of third order forces and moments with wave number and drafts of cylinders.
It is believed that the third or higher order forces are the exciting sources for ringing responses of tension leg platforms (TLP's) and gravitybased structures (GBS). Recently, number & researches have been carried out for predicting third order surge forces on cylinders. Based on the phenomenon that ringing occurs in long waves, Faltinsen, Newman and Vinje (1995) proposed a slender cylinder theory. In such a long wave regime, the second order diffraction can be neglected, and the third order surge force is predicted by a kind of extension of Morison equation. The attempt on full diffraction theory in the frequency domain was firstly made by Malenica and Molin (1995). They developed a semi-analytic solution for uniform cylinders in finite water depth, and computed the third order surge forces on them successfully. Yeng and Kato (1996) developed a numerical model for axisymmetric bodies by an integral equation method, which is capable for third order surge forces, heave forces and pitch moments. Kim (1998) developed a method for solving the full nonlinear wave diffraction from a uniform cylinder in the time domain. The third order surge forces are obtained by a Fourier analysis of the time history of full nonlinear wave forces.
