A first-principles derivation procedure for wake-body models in vortex-induced vibration: Proof-of-concept

A generalized variational equation based on the extended Hamilton's principle is presented as the starting point for a procedure from which wake-body models for the two-dimensional vortex-induced vibration of a cylinder can be derived. The case of an elastically mounted cylinder with a transverse degree-of-freedom in a uniform flow is offered as a “model problem” through which this derivation procedure is illustrated. A number of wake-body models from the literature are shown to be recoverable from the more general model derived here. The correspondence with these “classical” models is presented as evidence of the feasibility of incorporating this methodology into vortex-induced vibration modeling. Unlike these comparison models, however, which are often assigned an ad hoc form, any assumptions made in arriving at the derived wake-body model are explicitly stated.