This paper deals with the relationship between hydroelasic response and bending stiffness distribution of thin plate floating on shallow water in waves. Firstly, a calculation method by which the effect of bending rigidity distribution can be considerable is proposed. The Weighted Residual Method is employed to the dynamic condition of floating thin plate. As a result of integration by parts, a new finite element equation which contains the effects of water pressure is derived. This equation implies one more nodal variable except deflection and slope, one more nodal force except shearing force and bending moment. We adopt the analytical solution of dominant equation as a displacement function of the element. Next using this new hydroelastic element, some calculations for parametric stiffness distribution are carried out. Some cases in which the response of floating thin plate in waves can be efficiently reduced are shown.
The analytical solution of a beam floating on shallow water in waves had been shown by Stoker (1957). Namba and Ohkusu (1999) extended Stoker's method to a semi-infinite plate and showed some characteristics of VLFS in waves, for example, the refraction, critical incident angle and relationship between transmitted wave amplitudes and response of VLFS and so on. On the other hand, Fujikubo et al (1997) had shown the FEM in which the dynamic displacement function consisting of the analytical solution of a beam on elastic foundation is used. Getting inspirations from their work, in this paper we propose the FEM using a dynamic displacement function for the hydroelastic problem of a beam floating on shallow water in waves. Our dynamic displacement function consists of the Stoker's solution which contains effects of water pressure and deflection of the beam. The Weighted Residual Method derives what new nodal data are.
