Dynamics of rigid bodies in fluid and limit eigenmodes; theoretical research

Abstract

Interaction between ideal incompressible fluid and a rigid body, submerged into the fluid, is investigated. If rigid bodies are not fastened together by mechanical con-nections the interaction of the bodies is possible only if the fluid is present. The case when several bodies are identical and their supports are the same is investigated: eigenfre-quencies of these bodies in vacuum coincide. If density of the fluid approaches zero then all eigenfrequencies of the structures in the fluid approaches eigenfrequencies of the same structures in vacuum. In the paper it is given a proof that eigenmodes in the fluid can be completely different from eigenmodes in vacuum and do not approach eigen-modes in vacuum. The reason of this paradoxical distinc-tion between the eigenfrequencies and the eigenmodes is presented. It is revealed, that the limit eigenmodes and the vacuum eigenmodes are different when eigenfrequencies of several bodies in vacuum coincide. This investigation can be significant if forced vibrations frequency of such me-chanical system is resonant.