Nonlinear dynamic analysis of a cable under first and second order parametric excitations

It is well known that small periodic vibrations of a cable support through its axial direction produce large spectacular oscillations of the cable. This may occur when the frequency of the anchorage motion is close to the first natural frequency or twice the fundamental frequency of the cable. In this paper, a nonlinear dynamic study of a cable under first and second order parametric excitations is presented. The cable model takes into account sag as well as quadratic and cubic nonlinear couplings between in-plane and out-of-plane motions. As a numerical example, a single-d.o.f. planar model of a horizontal cable is used to study the effect of frequency and amplitude of excitation as well as the natural damping of the cable on its transient and steady state responses with a particular focus on the time needed to trigger first and second order parametric resonance