To solve the problems of vibration of a deformable elastic body containing a liquid with a free surface or interacting with a limited amount of fluid on the part of its border under the action of a gravitational field, a correct and consistent formulation of the boundary conditions at the interface of dissimilar media is necessary. A mathematical formulation of the relations at the contact surface of the two media is proposed, which is invariant with respect to a curvilinear coordinate system on the surface based on the vector form of equations. The variational principle of a mixed type has been formulated that allows effective application of three-dimensional finite element models to solve the problems and development of appropriate algorithms.
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