In this paper we consider vibrations of the baffled elastic fuel tank partially filled with a liquid. The compound shell was a simplified model of a fuel tank. The shell is considered to be thin and the Kirchhoff-Love linear theory hypotheses are applied. The liquid is supposed to be an ideal and incompressible one and its flow introduced by the vibrations of a shell is irrotational. The problem of the fluid-structure interaction was solved using the reduced boundary and finite element methods. The tank structure was modeled by the FEM and the liquid sloshing in a fluid domain was described by using the multi-domain BEM. The rigid and elastic baffled tanks of different forms were considered. The dependencies of frequencies via the filling level were obtained numerically for vibrations of the fluid-filled tanks with and without baffles. Keywords: baffles, fluid-structure interaction, free vibrations, liquid sloshing, multi-domain boundary element method, systems of singular integral equations.

The paper presents a fluid-structure interaction analysis of fuel tanks with cylindrical and spherical compartments partially filled with a liquid. The compound shell of revolution is considered as a container model. The shell is supposed to be thin, so the Kirchhoff-Love linear theory hypotheses are applied. The liquid is an ideal and incompressible one. Its properties and filling levels may be different within each compartment. The shell vibrations coupled with liquid sloshing under the force of gravity have been considered. The tank structure is modelled by a finite element method, whereas liquid sloshing in the compartments is described by a boundary element method. A system of singular integral equations is obtained for evaluating the fluid pressure. At the first stage, both spherical and cylindrical fluid-filled unconnected rigid shells are considered. Different filling levels as well as small radii of free surfaces are taken into account in problems of liquid sloshing in spherical shells. The sloshing frequencies in the presence of complete or partially covered free surfaces are determined for cylindrical shells. The boundary element method has proven to be effective and accurate in all the problems considered. At the second stage, the natural frequencies and modes of the dual compartment tank are obtained including sloshing, elasticity, and gravity effects.

A new numerical approach is proposed to address problems of free liquid vibrations in axisymmetric compound rigid shells using a singular boundary method. The liquid is supposed to be perfect and incompressible, and its flow is irrotational so the liquid velocity can be presented as a potential gradient. The approximation of a small fluid surface elevation is used, and the free surface function is presented as a sum of the fluid-filled shell height and the small elevation function. A series expansion of the potential function about stationary states is used. To find the stationary states, an eigenvalue problem is formulated. Eigenvalues and eigenvectors are obtained using the singular boundary method with the origin intensity factor as the singular integral over the singular boundary element. The numerical results for free vibration analysis of cylindrical shells, obtained by singular boundary method and direct boundary element methods, are compared. Different compound rigid shells are considered in numerical simulations of free liquid vibrations.

The paper presents an approach based on reduced boundary element methods to resolve axisymmetric problems in potential and linear isotropic elasticity theories. The singular integral equations for these problems are received using fundamental solutions. Initially three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So the three-dimensional axisymmetric problems are reduced to systems of singular integral equations requiring the evaluation of linear integrals only. The fundamental solutions and their derivatives are expressed in terms of complete elliptic integrals. The effective algorithm for treatment of the singular integrals is proposed. The multi-domain boundary element method is applied for the numerical simulation. As examples, the following problems are considered: fluid induced vibrations of a compound cylindrical-spherical elastic shell partially filled with an ideal incompressible liquid, and axisymmetric elasticity problems for an isotropic body with rigid or elastic circular cylindrical inclusions.

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