On wave motion due to rolling of a submerged thin vertical plate

Abstract

The use of Havelock's expansion of water wave potential in the study of wave motion set up due to small rolling oscillations of a thin vertical plate submerged in deep water gives rise to a singular integral equation involving a combination of logarithmic and Cauchy-type kernel in a double interval. Its solution is obtained in a straightforward manner, wherein the Plemelj formula is suitably utilized in the analysis. The amplitude of wave motion at large distances from the plate and the velocity potential are obtained explicitly for this problem.