Abstract
We investigate theoretical aspects of a reduced-order model for transverse galloping, which is derived directly from the full governing equations, i.e., the fluid mass and momentum balances, the fluid far-field boundary condition, the kinematic and dynamic conditions at the interface, and the bluff body equation of motion. We show that the presence of low-intensity turbulence and back-action from the slow transverse oscillations of the bluff body yield a correction to the hydrodynamic force of the quasi-steady theory in the form of additive random excitation. The reduced-order model consists of a pair of nonlinear Langevin equations for the amplitude and phase of the transverse motion of the bluff body. We show that while the phase dynamics is associated with a strongly diffusive random walk motion, the amplitude dynamics is associated with a relatively weak diffusion and can be mapped onto the motion of an overdamped particle trapped in a potential well. This mapping provides a highly useful tool for understanding both the deterministic (no random excitation) and the stochastic (weak random excitation) amplitude dynamics, and hence, for yielding theoretical insights on the overall system dynamics.
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Notes
Under the assumption that \(U^*\gg St^{-1}\); otherwise, when \(U^*\sim \ St^{-1}\), vortex-induced vibration can occur [39].
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Shoshani , O. Theoretical aspects of transverse galloping. Nonlinear Dyn 94, 2685–2696 (2018). https://doi.org/10.1007/s11071-018-4518-1
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DOI: https://doi.org/10.1007/s11071-018-4518-1