ON THE QUASI-STEADY ANALYSIS OF ONE-DEGREE-OF-FREEDOM GALLOPING WITH COMBINED TRANSLATIONAL AND ROTATIONAL EFFECTS

Galloping is the low-frequency, self-excited oscillation of an elastic structure in a wind field. Its analysis is commonly based on a quasi- steady aerodynamic analysis, in which the instantaneous wind forces ar e derived from force data obtained in static wind tunnel tests. For th e galloping of a rigid prismatic beam the validity of the quasi-steady assumption is critically assessed for the case that rotational effect s must be included in the aerodynamics. An oscillator structure with o ne (torsional) degree of freedom is proposed which allows a reliable m odelling. Its effective motion can be considered as being composed of a translation with a coupled rotation of the cross section, and can be regarded as a natural extension of pure translational galloping. The analysis reveals that the resulting aerodynamic damping is determined by the sectional aerodynamic normal force coefficient alone. An aerody namic damping coefficient is defined that can be expressed uniquely in terms of an aerodynamic amplitude, allowing a normalization of the ga lloping curve. This result can be used to analyze both purely translat ional and combined galloping, which are found to differ only by the wa y the structural amplitude (displacement) is related to the aerodynami c amplitude. An interesting result is that for large wind speeds rotat ional galloping displays an aerodynamic limit, in contrast to translat ion galloping where the limit-cycle amplitude increases linearly with wind speed. Results obtained from wind tunnel experiments confirm the major findings of the analysis.