Combined effect of boundary conditions and longitudinal distance on FSI of a flexible plate behind a circular cylinder

The interaction between the wake of a circular cylinder and a flexible plate represents a fundamental FSI problem. Prior research has primarily focused on configurations in which the plate's leading edge (LE) is rigidly clamped, while scenarios involving elastic boundary conditions at the LE have been comparatively underexplored. In the present study, the governing equations for a flexible plate with elastic boundary conditions are formulated, and a corresponding FSI numerical solver is developed. To validate the accuracy of the proposed approach, mesh resolution independence studies and numerical validations are conducted. Analysis of the plate's oscillation amplitude reveals that, as the longitudinal distance x∗ increases, the amplitude initially decreases within the near-wake region, subsequently experiences a sudden increase and stabilization in the strong-coupling region, and finally diminishes in the far-wake region. This behavior is observed regardless of whether the LE is elastically restrained or rigidly clamped. Within the weak-coupling zone, the oscillation amplitude decreases with increasing LE boundary stiffness. Conversely, in strong-coupling zone, the vibration amplitude remains nearly insensitive to LE stiffness. These findings clarify how plate oscillations can be regulated by tuning the boundary stiffness and longitudinal distance, providing guidance for vibration suppression or oscillation-based energy harvesting in engineering applications.