Many analytical methods have been proposed to calculate hydroelastic responses of a very large pontoon-type floating structure in waves. In this paper, variational principles considering wave radiation condition at infinity related to motions of a plate in waves, which are very important in calculations of the elastic response of the pontoontype floating structure, are discussed. First, Sommerfeld radiation condition at infinity is extended to treat a case with an incident wave. Second, four kinds of variational principles related to motions of the elastic floating plate on a water surface considering the incident and radiated waves are proposed and clarified the mutual relationship of these variational principles. Third, numerical results for elastic response of a floating plate of rectangular and L-shaped plan geometry in waves, which are obtained by using these proposed variational principles, are shown.
A Pontoon-type VLFS is one of the typical structural types of very large floating structures (VLFS). Various numerical methods have been proposed to predict the hydroelastic response of this structure in waves (Watanabe (2004); Chen (2006)). These methods are classified into the modal expansion method and the direct method. These analyses are carried out in the frequency domain or in the time domain. Finite element method is used for the structure in order to analyze actual complicated floating structure (Seto et al. (1998); Utsunomiya et al. (2002)). In relation to the elastic response of Pontoon-type VLFS in waves, four kinds of variational principles related to elastic motions of such a floating plate were derived and made clear the mutual relationship of them (Isshiki (2000), Isshiki and Nagata(2001)). However, in these variational principles, wave radiation condition at infinity was not included and the normal velocity on a vertical cylinder surface of finite size surrounding the plate was designated.