Nonlinear mathematical modeling and inversion dynamic identification of galloping aerodynamics with time-lag correction

Galloping instability presents significant risks to slender bluff structures. Classical polynomial models for galloping analysis are limited by their inability to capture unsteady time-lag effects, the generation of high-frequency artifacts, and symmetry constraints. To overcome these shortcomings, this study addresses these limitations by proposing a fundamental-frequency-projected galloping model with time-lag correction. Concurrently, a dynamic inversion identification (DII) method is proposed, enabling the isolation of self-excited forces from free vibration data solely based on displacement signals. A key to this method is the preprocessing of displacement data with an ideal self-excited response function, effectively eliminating experimental noise and non-self-excited interference. The efficacy of the proposed framework is confirmed by validation through numerical simulations on 2:1 rectangular cylinders and wind tunnel dynamic experiments on a complex engineering section. The results demonstrate that the new model successfully addresses asymmetry and time-lag effects while suppressing spurious high-frequency output. Furthermore, the DII method, empowered by its preprocessing step, proves to be an effective tool for force identification in tests. Integrating the proposed model with the equations of motion allows for accurate mapping of stability boundaries and prediction of post-critical behavior, even with a minimal-order model.