Motions of elastic solids in fluids under vibration

Motion of a rigid or deformable solid in a viscous incompressible fluid and corresponding fluid–solid interactions are considered. Different cases of applying high frequency vibrations to the solid or to the surrounding fluid are treated. Simple formulas for the mean velocity of the solid are derived, under the assumption that the regime of the fluid flow induced by its motion is turbulent and the fluid resistance force is nonlinearly dependent on its velocity. It is shown that vibrations of a fluid’s volume slow down the motion of a submerged solid. This effect is much pronounced in the case of a deformable solid (i.e., gas bubble) exposed to near-resonant excitation. The results are relevant to the theory of gravitational enrichment of raw materials, and also contribute to the theory of controlled locomotion of a body with an internal oscillator in continuous deformable (solid or fluid) media.