Variational principles for fluid-solid interactions, with application to ship beams

Abstract

The purpose of this paper is threefold: (1) To derive the unconstrained variational principles which treat initial and boundary value problems of fluid-solid interactions in a unified manner, then by using it (2) to establish the one-dimensional governing equations of vibrations of ship beams immersed in an ideal fluid, and also (3) to examine the uniqueness in solutions of these equations. First, a general principle of physics (Hamilton's principle) is transformed so as to derive the variational principles through the dislocation potentials and Lagrange multipliers. Next, the variational principles together with the generalized Mindlin method of structures are used to construct the governing equations by expanding the displacement components and the hydrodynamic pressure in series. The governing equations are coupled with the pressure field and incorporate all the effects of transverse shear and normal strains and the rotatory inertia, and they accommodate all the types of extensional, flexural, and torsional motions of ship beams. Also, the uniqueness is examined, and the sufficient conditions are enumerated for it. [Work supported by TÜBİTAK.]