Fluid-structure interaction of a flexible plate with elastic boundary conditions in the wake of a circular cylinder

The fluid-structure interaction (FSI) of a flexible plate in the wake of a circular cylinder is a classical problem. Notably, the majority of prior studies have focused on configurations where the plate leading edge (LE) is fixed, and the trailing edge (TE) is free. In contrast to conventional approach, the present study imposes elastic boundary conditions at both the LE and TE of the plate. To reveal the oscillating law of the flexible plate with elastic boundary conditions, the governing equations describing structural vibrations with elastic constraints are derived, alongside the FSI computational procedures. The accuracy of the numerical predictions of flow field is validated against published results, with good agreement achieved. Findings reveal that the plate exhibits increased oscillatory tendencies when the fixed LE is replaced by an elastic boundary. Among the elastic components considered, translational springs exert a more significant influence on the plate's oscillation than rotational springs. Moreover, larger deformation is observed when the TE possesses moderate elasticity (k₂ = 2 × 10⁴ N/m², and K₂ = 2 × 10⁴ N), irrespective of the boundary stiffness of the LE. This investigation offers valuable insights for practical applications aimed at either suppressing oscillations or harnessing oscillatory energy in flexible plates through the manipulation of boundary conditions.