On the Description of Non-Harmonic Wave Problems in the Frequency Domain (5th Report) Comparisons of Methods for Transient Responses of a Ship in Waves

Abstract

In the field of ship maneuvring, the description of transient responses of a ship has received the most attention to assess the ability of ship's rudder to control the ship. On the contrary, for seakeeping problems, ship responses in waves have been expressed in terms of amplitude and phase in a steady state and the transient description has not been popular so far. However, the description of the transient response of a ship is recognized to be important in dealing with the problems, such as the responses of a moored body under the combined action of waves and/or stepwise wind forces. According to a survey of the literature concerning the transient responses of a ship, the following four approaches are considered for the practical use: (1) second-order linear differential equation with constant coefficients. (2) frequency response corresponding to a Fourier integral approach. (3) impulse response corresponding to a Fourier integral approach. (4) integro-differential equation with memory effect fuction. (5) higher order differential equation The purpose of this paper is to find the best calculation method among the five methods, in a practical sense, to describe the transient motion in waves. For this purpose, firstly, the authors discuss theoretically the relationship among the methods and point out some problems appeared in the procedure of numerical calculations. By this process the 4th method is chosen as a preferable one to describe transient responses. Secondly, the authors discuss the approximate evaluation method for the memory effect functions which are involved in the integro-dfferential equation.