On the heaving motion of a circular cylinder more or less than half immersed in the free surface of a fluid

Résumé fourni par la source

Abstract We consider a problem in the linearized theory of water waves. A smooth oscillating two-dimensional body meets the free surface at angles other than right-angles. In this paper we prove the existence of a solution for this problem by using integral equations. This problem has been considered by other authors; however, their attempts have resulted in singular integral equations. To show that Fredholm theory applies to these equations involves a great deal of generalized analysis. It is shown that it is possible to obtain a well-behaved integral equation by means of an explicit modification of the source potential used to derive this equation. To illustrate this method a circular cylinder that is more than or less than half immersed and undergoing a heaving motion is considered. This method is in terms of more elementary concepts than those used by previous authors. The explicit proof also indicates how the problem may be solved in practice, and it is hoped to report on the numerical solution later.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.