Dynamic instability of inclined cables under combined wind flow and support motion

"In this paper an inclined nearly taut stay,. belonging to a cable-stayed bridge, is considered. It. is subject to a prescribed motion at one end, caused. by traveling vehicles, and embedded in a wind flow. blowing simultaneously with rain. The cable is modeled. as a non-planar, nonlinear, one-dimensional continuum,. possessing torsional and flexural stiffness. The. lower end of the cable is assumed to undergo a vertical. sinusoidal motion of given amplitude and frequency.. The wind flow is assumed uniform in space. and constant in time, acting on the cable along which. flows a rain rivulet. The imposed motion is responsible. for both external and parametric excitations,. while the wind flow produces aeroelastic instability.. The relevant equations of motion are discretized via. the Galerkin method, by taking one in-plane and one. out-of-plane symmetric modes as trial functions. The. two resulting second-order, non-homogeneous, timeperiodic,. ordinary differential equations are coupled. and contain quadratic and cubic nonlinearities, both in. the displacements and velocities. They are tackled by. the Multiple Scale perturbation method, which leads. to first-order amplitude-phase modulation equations,. governing the slow dynamics of the cable. The wind. speed, the amplitude of the support motion and the internal. and external frequency detunings are set as control parameters. Numerical path-following techniques. provide bifurcation diagrams as functions of the control. parameters, able to highlight the interactions between. in-plane and out-of-plane motions, as well as. the effects of the simultaneous presence of the three. sources of excitation."