Periodic and quasiperiodic galloping of a wind-excited tower under external excitation

The galloping of tall structures excited by steady and unsteady wind may be periodic or quasiperiodic (QP) with amplitudes having the same order of magnitude. While the onset of periodic and QP galloping was studied, their control on the other hand has received less attention. In this paper, we conduct analytical study on the effect of a fast harmonic excitation on the onset of periodic and QP galloping in the presence of steady and unsteady wind. We consider the cases where the unsteady wind activates either external excitation, parametric one or both. A perturbation analysis is performed to obtain close expressions of QP solution and the corresponding modulation envelopes. We show that at various loading situations, the periodic and QP galloping onset is significantly influenced by the amplitude of the fast external excitation. In the case where the unsteady wind activates parametric excitation, the QP galloping occurs with higher frequency modulation compared to the case where the unsteady wind activates external excitation. In the case where external and parametric excitations are activated simultaneously, fast harmonic excitation eliminates bistability in the amplitude response and gives rise to a new small QP modulation envelope.