Numerical evaluation of coupled galloping of slender towers in boundary-layer winds based on a nonlinear analytical model

Slender towers with certain shapes of cross-section can exhibit galloping that involves coupling between the oscillation components about the principal structural axes. This study presents a nonlinear analytical model of this type of galloping for towers subjected to winds in the atmospheric boundary layer. The formulation of the model adopts the assumption of quasi-steady wind loading. However, this formulation differs from those for the classical across-wind galloping in that it does not require the wind to be along the direction of a principal structural axis. In addition, it considers the oscillation components about both structural axes, instead of only the across-wind oscillation, to enable the evaluation of the coupling between the components. Further, because the formulation does not linearize the wind-induced force acting on the structure based on the assumption of small vibration amplitude, the resultant model can be used as a basis to numerically assess the amplitudes and frequencies of large-amplitude coupled galloping oscillations. In an illustrative application, the model is used to evaluate the wind-induced vibration of a full-scale slender tower. The wind fields are simulated using the spectral representation method, and the responses of the structure to the simulated wind excitation are obtained by numerically solving the nonlinear differential equations representing the model. The results of the numerical evaluation are compared with the corresponding field observations to validate the effectiveness of the model, and the validated model is used to investigate the effects of the structural damping and the turbulence intensity of wind on the characteristics of the coupled galloping of the tower.