A unified framework for rectilinear and rotational flow-induced vibrations of a square prism

A unified framework is developed in this study to investigate the flow-induced vibrations of a square prism along a circular trajectory, bridging the gap between rectilinear and rotational flow-induced vibrations (FIVs) and aiming to offer an interconnected perspective for understanding the underlying physical mechanisms of fluid-structure interactions. Comprehensive analyses of the vibration responses, phase portrait evolutions, vortex shedding patterns, work-energy characteristics, and surface pressure distributions of the square prism undergoing vortex-induced vibration and galloping are conducted using this framework and validated against experimental data. The above analyses over a wide range of trajectory radii spanning from 0.1 D to 100 D (where D denotes the side length of the square prism) and a broad variety of airflow velocities ranging from 0.1 m/s to 3.0 m/s, are performed for concave and convex configurations corresponding to equilibrium circular trajectory angles of 0^° and 180^°, respectively. Three principal observations are obtained. The introduction of a finite trajectory radius R results in configuration-dependent dynamical evolution pathways from rectilinear (R→∞) to rotational (R = 0) FIVs. For the concave configuration, the flow-body system sequentially undergoes galloping for R/D > 2, forced vibrations for 0.2 ≤ R/D ≤ 2, and classical vortex-induced vibrations (VIVs) at R = 0. In contrast, the convex configuration demonstrates three distinct dynamic regimes: galloping for R/D ≥ 2, subharmonic VIV for 0.4 ≤ R/D ≤ 1, and classical VIV for R/D ≤ 0.2. Moreover, the subharmonic VIV regime is characterized by the emergence of an upper branch triggered by a 2P (two-pair) wake mode and a higher branch triggered by either a 4(2S) or 6(2S) wake mode, corresponding to four or six successive two-single vortex shedding patterns within each oscillation cycle. Additionally, the excitation mechanism underlying FIVs is dictated by the sign of aerodynamic work: positive work gives rise to large-amplitude synchronization branches, whereas negative work leads to small-amplitude desynchronization branches.