Modelling nonlinear aerodynamic damping during transverse aerodynamic instabilities for slender rectangular prisms with typical side ratios

Abstract

The transverse aerodynamic instabilities of rectangular cylinders with three typical side ratios (width-to-depth-ratio as 2:1, 1:1 and 1:2) were investigated through a series of elastically-supported sectional model tests. Experimental results indicate that side ratio plays an important role in the phenomena of transverse instabilities and a larger side ratio B/D generally corresponds to a stronger interaction of VIV and galloping. For side ratio B/D ​= ​2, all test cases exhibited unsteady galloping starting from the Kármán vortex resonance wind speed. When Scruton number is larger than a threshold value between 12.1–19.4, the unsteady galloping of B/D ​= ​1 shows a separate behavior of VIV and galloping with a twofold-amplitude phenomenon. Whereas, side ratio B/D ​= ​0.5 exhibited a pure transverse VIV. The feasibility of classical quasi-steady theory was found not able to predict the onset wind speeds and stable amplitudes. An empirical model was established to consider the aerodynamic nonlinearity by two amplitude-dependent damping terms and aerodynamic unsteadiness by expressing aerodynamic parameters as functions of reduced frequency. The empirical model was validated, having a satisfactory accuracy in predicting the vibration amplitudes of unsteady galloping and VIV. The proposed model represents a promising tool in engineering applications where the interference of VIV and galloping is concerned.