Galloping Instabilities of Geometrically Nonlinear Nonshallow Cables Under Steady Wind Flows

Abstract

A geometrically exact mechanical model of nonshallow elastic cables subjected to aerodynamic forces generated by the mean wind velocity field is discussed. The linearization around the catenary configuration leads to the prediction of the critical galloping velocities and the critical modes accomplished employing the Routh-Hurwitz theorem. Then, the post-critical responses, past the pitchfork bifurcation occurring at the galloping critical condition, are constructed via an asymptotic treatment of the equations of motion. Bifurcation diagrams of the post-critical vibration amplitude for various sag-to-span ratios are computed to investigate the dependence of the post-critical galloping regime on the prestress level in the cable.

Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams

“…More recently, they have extended the method to infinite dimensional system, to analyze divergence, Hopf and doublezero bifurcations [19][20][21][22]. The method is based on the direct treatment of the original (integro)-differential equations, avoiding any a priori discretization (as that, e.g., performed in [3]), according to the so-called direct method, widely applied by Nayfeh and co-workers [23][24][25], and many other authors (see, e.g., [26,27]), to several problems of non-linear dynamics.…”