An Extended Nonlinear Wake-Oscillator Model for Coupled Aeroelastic Response of Slender Structures

Nonlinear aeroelastic instabilities play a key role in the response of slender civil engineering structures exposed to wind, particularly in situations where multiple mechanisms such as vortex-induced vibration and galloping may interact. Wake-oscillator models provide a physically motivated framework for describing these phenomena by introducing additional variables representing the near-wake dynamics. In this work, a combined heave–pitch–wake model is formulated by extending the wake-oscillator framework of Mannini et al. to include an additional rotational degree of freedom. The resulting system is intended to describe the coupled interaction between translational and torsional motion, with particular relevance to cable-like structures where torsional effects may influence fatigue behavior, especially under conditions of geometric irregularity. The governing equations are derived in dimensionless form and analyzed using a harmonic balance approach in the slow-time formulation, leading to a system of slow-time equations and their stationary counterpart. The formulation retains quasi-steady aerodynamic forces in implicit form, allowing the direct use of experimentally identified characteristics.