On the Description of Non-Harmonic Wave Problems in the Frequency Domain (7th Report) : Memory Effect Functions for a Two-Dimensional Body of Arbitrary Shape

Abstract

In this paper, the calculation method of the memory effect functions which is mentioned in the 1st report for Lewis form sections is extended to solve the problem for more complicated shapes. As was shown in the 1st report, the memory effect functions are expressed by the integration of the damping force coefficients or wave amplitude ratios from zero to an infinite frequency. The wave amplitude ratios for all frequencies are obtained by connecting the exact values of the wave amplitude ratios in a medium frequency range with the asymptotic values in a high frequency range. The exact hydrodynamic coefficients as we11 as the wave amplitude ratios for an arbitrany shape are calculated by the method of conformal mapping developed by Takagi. The transformation coefficients are determined by using the Fourier expantion method which is similar to the one used for a wing section of the aeroplane. The asymptotic values of the wave amplitude ratios in a high frequency range are given by solving the high frequency boundary value problem. The method presented here is the extention of the Ursell's for forced heaving circular cylinder. Numerical calculations of the memory effect functions are carried out for the inclined ship sections.