| Abstract: | Convergence criteria are provided for truncating the evanescent eigenmode series in the Green's function for vertical, axisymmetric bodies of revolution. To numerically compute the strength of the source distribution for both the exciting and restoring forces, separate criteria are required for the off-diagonal and for the diagonal elements in the matrix of coefficients for the source strengths. The Black-Fenton algorithms for wave-induced exciting forces on vertical axisymmetric bodies of revolution are extended to include the wave-induced restoring forces. The Gauss-Seidel matrix version method recommended by Fenton is compared with the Gauss elimination method and is found to be non-converging for near deep water wave conditions. Comparison between theory and measured data for the dynamic response of a discus buoy demonstrates the convergence criteria over a range of dimensionless frequencies in relatively deep water wave conditions. |
