Non-linear dynamics of an elastic cable under planar excitation

The phenomena of the finite forced dynamics of a suspended cable associated with the quadratic and cubic non-linearities in the equations of motion are studied. A high-order perturbation analysis for the primary resonance is accomplished and numerical results are presented for the frequency-response equation and the region of instability of the steady-state solutions. Multivaluedness of the response curves is shown to occur with different characteristics depending on the cable and forcing parameters. The dependence of the response on the initial conditions is examined by means of the trajectories of the unsteady-state motions.