Contact interaction of a bounded liquid volume with a solid under the action of gravity forces

A mathematical model of the interaction between a bounded liquid volume and a deformable solid under the action of a homogeneous gravitational field is developed. With this model, small vibrations of the hydroelastic system are studied. The mathematical formulation of the contact relations on the interface used is invariant to the curvilinear coordinates system introduced on the interface and is based on equations in vector form. A variational principle of mixed type is formulated which permits creating necessary prerequisites for finite-element models to be efficiently used to solve the problem and for the development of appropriate algorithms. An example of a liquid-solid system is studied which is sensitive to the proper consideration of the interaction factors determined by the action of the gravitational field.