Periodic and quasiperiodic galloping of a wind-excited tower under parametric damping

The effect of internal parametric damper on periodic and quasi-periodic (QP) galloping of a wind-excited tower is studied analytically in this paper. We use a simple degree of freedom model and consider the cases where the turbulent wind activates external excitation, parametric one or both. The method of three stage perturbation analysis is performed to obtain an approximation of periodic and QP solutions as well as the QP modulation envelope. We explore the effect of internal parametric damping (PD) on the amplitude and the onset of periodic and QP galloping. It is revealed that for specific turbulent wind excitation, the PD significantly influences the critical wind speed above which periodic and QP galloping occurs. In the case where external and parametric excitations are activated simultaneously, QP galloping persists for all ranges of wind velocity. The results also show that the modulation frequency of the QP galloping depends strongly on the type of excitation induced by the turbulent wind.