Bifurcation and stability of a two-tower system under wind-induced parametric, external and self-excitation

A two-degree of freedom nonlinear system, describing the dynamics of two towers exposed to turbulent wind flow and linked by a nonlinear viscous device, is considered. The steady component of the wind is responsible for self-excitation, while the turbulent part causes both parametric and external excitations, considered in a specific resonance condition. The possible occurrence of multiple Hopf bifurcations is taken into account. The periodic and quasi-periodic solutions are studied after applying a perturbation scheme. The effect of the viscous device on the dynamics of the structure is analyzed, in order to investigate its effectiveness in mitigating the oscillations of the two independent towers.