Fluid-Induced Vibration Frequency and Damping of a Coaxial Cylinder in a Quiescent Viscous Medium: Theoretical and Numerical Predictions

Abstract This study, motivated by applications in nuclear engineering, examines the fluid-induced vibrations of a flexible inner cylinder concentrically positioned within a rigid outer cylinder, separated by a quiescent Newtonian viscous fluid. Building on our previous work, which focused on forced motions, we extend the theoretical formulation to account for vibrations induced by fluid forces. A new expression for the linear fluid force is derived, introducing a fluid transfer function that depends on key dimensionless numbers such as the aspect ratio, radius ratio, and Stokes number. The vibration frequency and viscous decay rate are predicted by coupling this force with an Euler–Bernoulli beam model and using a modal decomposition based on a complex angular frequency. A computational approach is also developed, integrating an explicit partitioned coupling scheme into the open-source triocfd software. This method enables efficient numerical simulations of the fluid–structure interaction, ensuring internal coupling without excessive data exchange. Comparisons between theoretical predictions and numerical results show excellent agreement for pinned-pinned and clamped-clamped configurations across specific Stokes number and density ratio values. Additionally, the validity of the proposed theory and numerical simulations is further confirmed by comparisons with experimental data from the literature, showing strong consistency for a clamped-free configuration. A parametric study including variations of the Stokes number is eventually also performed, demonstrating the robustness and applicability of the theoretical and numerical approaches.