Estimation of stochastic crosswind response of wind-excited tall buildings with nonlinear aerodynamic damping

This study addresses the analysis of crosswind response of tall buildings and flexible structures at wind speed region higher than the vortex lock-in speed, where nonlinear negative aerodynamic damping effect is significant. The modeling of nonlinear aerodynamic damping as a function of time-varying velocity and/or displacement of vibration is established based on motion-induced aerodynamic force information obtained from forced-vibration model testing in wind tunnel, referred to as harmonic balance. Response time history simulations are performed by solving the nonlinear equation of motion to explore the unique hardening non-Gaussian characteristics of crosswind response and its extreme value distribution with reduced peak factor. The response time history simulations also provide a bases for assessing the performance of analytical predictions of root-mean-square (RMS) response using crosswind loading spectrum and equivalent aerodynamic damping models. The limitations of the equivalent aerodynamic damping models as functions of RMS response derived from harmonic balance and statistical linearization with an assumption of Gaussian response are revealed. This study, at the first time, by using the method of equivalent nonlinear equation, presents complete analytical solutions of crosswind response statistics, including not only the RMS response, but also response kurtosis, response probability distribution, peak factor and extreme value distribution. The comparison of the analytical predictions with response simulation results illustrates that the method of equivalent nonlinear equation is very accurate in predicting crosswind response statistics that are influenced by the nonlinear aerodynamic damping. The narrow band feature of response is further considered in this study in the calculation of crossing rate using amplitude process, which leads to even better predictions of extreme statistics. This general framework can also be readily adopted in design codes and standards for calculating vortex-induced vibration of towers and chimneys.