New approach for solving the fluid–structure interaction eigenvalue problem by modal analysis and the calculation of steady-state or unsteady responses

This report focuses on an analysis of the dynamic behaviour of a fluid–structure interaction system. This analysis is nonlinear, and the modal behaviour depends on many parameters, because large displacements are assumed. Technical applications include vibration of blades of rotational centrifugal pumps or water turbines. A new mathematical model of a boundary condition that allow for modal analysis and calculation of the steady state or unsteady state responses is presented in this article. This condition is based on a special convolutory integral for fluid velocity and pressure and their expansion into a series of eigenmodes of structure vibration. This approach allows for the separation of the structure and the fluid. A comparison between the computational and the experimental analyses is presented. Curvilinear coordinates and a Bézier body were chosen for the description of the geometrical configuration and the approximation of the solution.