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 of the contribution to third-order forces and moments from potentials at each wave order, and the relation of third-order forces and moments to wave number and drafts of cylinders.
It is believed that the third- or higher-order wave forces are the exciting sources for ringing responses of tension leg platforms (TLP) and gravity-based structures (GBS). Recently, a number of studies has 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 secondorder diffraction can be neglected, and the third-order surge force is predicted by a kind of extension of the Morison equation. The attempt at full diffraction theory in the frequency domain was first made by Malenica and Molin (1995). They developed a semi-analytic solution for uniform cylinders in finite water depth, and successfully computed the third-order surge forces on them. Teng and Kato (1996) developed a numerical model for axisymmetric bodies by an integral equation method, which works for thirdorder surge forces, heave forces and pitch moments. Kim et al. (1998) developed a method for solving the full nonlinear wave diffraction from a uniform cylinder in the time domain. The thirdorder surge forces are then obtained by a Fourier analysis of the time history of full nonlinear wave forces. This method is also available for higher-order wave forces.