Modeling the interference of vortex-induced vibration and galloping for a slender rectangular prism

Several bluff bodies in an airflow, such as rectangular cylinders with moderate side ratio, in particular conditions of mass and damping can experience the interference of vortex-induced vibration (VIV) and galloping. This promotes a combined instability, which one may call “unsteady galloping”, with peculiar features and possibly large vibration amplitudes in flow speed ranges where no excitation is predicted by classical theories. The mathematical model proposed between the 70's and the 80's by Prof. Y. Tamura to simulate this phenomenon was considered here for the case study of a two-dimensional rectangular cylinder with a side ratio of 1.5, having the shorter section side perpendicular to the smooth airflow. This wake-oscillator model relies on the linear superposition of the unsteady wake force producing VIV excitation and the quasi-steady force that is responsible for galloping. The model formulation was slightly modified, and the way to determine a crucial parameter was changed, revealing a previously unexplored behavior of the equations. In the present form, the model is able to predict the dynamic response of the rectangular cylinder with a satisfactory qualitative and, to a certain extent, quantitative agreement with the experimental data, although the limitations of the present approach are clearly highlighted in the paper. The mathematical modeling of unsteady galloping and the analysis of the results offer a deep insight into this complicated phenomenon and its nonlinear features. The model also represents a useful engineering tool to estimate the vibration of a structure or structural element for which the interference of VIV and galloping is envisaged.