Falling dynamics of flexible plates with concentrated weight

We investigate the free fall of a flexible plate with a concentrated central weight using numerical simulations to explore the coupling effects of structural flexibility and concentrated loading. Two-dimensional and three-dimensional (3-D) simulations, combining lattice Boltzmann and immersed boundary methods, identify four distinct falling modes: swing, stable falling, fluttering and tumbling. The swing and stable falling modes are reported for the first time in this context. By analysing the balance between bending stiffness upper K K $K$ and concentrated weight upper G G $G$ , we introduce a new dimensionless effective stiffness italic Kg equals upper K divided by upper G Kg = K / G $ \textit{Kg} = K/G$ , which governs mode transitions and successfully collapses the kinematic data. A bistable transition zone between fluttering and tumbling is observed, with the mode selection dependent on the initial inclination angle, which scales as a power law of italic Kg Kg $ \textit{Kg}$ . Additionally, within the swing mode, we observe a transition in wake topology from a 2P to a 2S vortex-shedding pattern, modulated by the mass ratio. In 3-D simulations, the finite aspect ratio upper A Subscript r A r $A_r$ significantly influences mode selection due to pressure leakage at the side edges. While the italic Kg Kg $ \textit{Kg}$ scaling remains valid for the global dynamics, 3-D effects suppress tumbling in narrow plates and induce spanwise oscillations in the stable falling mode at higher aspect ratios.