On the Influence of Irregular Frequencies in the Integral Equation Solutions of the Time-Dependent Free Surface Problems

Abstract

So far it has been known little about the problem for a 2-D general shaped body on free surface which makes arbitrary motion in time from t=0, though the problem might have broad application in ship hydrodynamics.As in the counterpart problem in the frequency domain appeared in the “strip method” or the “slender ship theory”, the problem in the time domain may have many solving methods. Among them the integral equation method seems to be most powerful. However, in solving the problem by source distribution method, one peculiar phenomenon occurs, that is, the irregular frequency effect in the time dependent source. This peculiarity is analysed theoretically by investigating the counterpart problem in the frequency domain.A procedure to avoid this peculiarity is presented, which is inherited from the results of Sayer & Ursell4) and Ogilvie & Shin.5) And a few attempts to the problem, making use of the integral equation methods, are illustrated in theories and numerical calculations.