A Time-Dependent Green Function and Sway Added Mass of a Rectangular Cylinder at Zero Frequency

Abstract

The order of passage to the limit in double limiting processes in a sway added-mass problem in water of finite depth is reversible and the double limit is finite. The author considers a two-dimensional rectangular cylinder floating in water of finite depth and oscillating in sway motion. When its frequency and depth-draft ratio approach zero and unity, respectively, the problem involves double limiting processes. The case for frequency first and then draft in the processes has been studied by Flagg and Newman [1]2. Here the reverse order is considered, namely, draft first and then frequency, and examine the limiting value analytically. Then reversibility of the order is discussed. For this purpose, a time-dependent Green function is employed. Green's function, in particular, may be convenient to use, for it can handle an arbitrary motion of the body. A system of linear integral equations in the limit is obtained. The kernel of the integral equation, when the draft tends to the depth of water, can be written as an eigenfunction expansion. Hence, the system of equations can be examined in a simple way. Lastly, it is shown that the present method using the time-dependent Green function indeed satisfies the radiation condition.