A kinematic method for the computation of the natural modes of Fluid-Structure Interaction systems

A kinematic approach is elaborated for Fluid-Structure Interaction (FSI) in linear conservative systems. It is based on the concept of added fluid field, which stands for the fluid displacement explicitly or implicitly associated with the structural displacement in a purely mechanical approach. The Lagrangian of a coupled system is hence written as the sum of the Lagrangian of the structure, the acoustic Lagrangian and a coupling Lagrangian expressed as the mass and stiffness-weighted scalar products of the acoustic field and the added fluid field. It is shown that the coupled modes of a fluid-structure system can be computed by combining its uncoupled modes, with a procedure involving symmetric matrices. Indicators of the coupling strength are provided: it is shown that strongly coupled systems do not exhibit large variations of their behavior when their uncoupled natural frequencies coincide, whereas weakly coupled systems do. Applications to some case studies of FSI are provided.