Nonlinear dynamics of a nearly taut cable subjected to parametric aerodynamic excitation due to a typical pulsatile wind flow

In this study, the dynamic response of a nearly taut nonlinear cable that is actuated by a pulsatile wind flow is investigated for the sake of obtaining the regime of motion and bifurcations of the system. The aerodynamic model is a general modelling of wind excitation including nonlinear cubic terms. Since realistic wind blows frequently and is not invariant, the velocity of the time -variant flow is considered to be a typical combination of a constant and a small harmonic perturbation. The equation of motion of the system has a simple form and is discretized by single -mode Galerkin method and by employing the method of multiple scales (MMS) the parametric resonance of the system is obtained. The results of bifurcations of the system assuming solely its first mode, exhibit a complicated behavior, whose occurrence in a simple dynamical system is interesting from the nonlinear dynamic point of view. Moreover, we show that as the frequency of the wind flow is decreased, the amplitude of the cable is also decreased. Also, as both constant and harmonic wind velocities are increased, the maximum amplitude of the system is not significantly influenced. Furthermore, the numerical-based bifurcation analyses show that for high values of constant wind velocity, small values of harmonic wind velocity, and excitation frequency, the system undergoes less chaos and actually unpredictable motions. The presented model can be evaluated more precisely to extend the above results to more realistic ones.