Numerical simulations of chaotic dynamics in a model of an elastic cable

The finite motions of a suspended elastic cable subjected to a planar harmonic excitation can be studied accurately enough through a single ordinary-differential equation with quadratic and cubic nonlinearities.The possible onset of chaotic motion for the cable in the region between the one-half subharmonic resonance condition and the primary one is analysed via numerical simulations. Chaotic charts in the parameter space of the excitation are obtained and the transition from periodic to chaotic regimes is analysed in detail by using phase-plane portraits, Poincaré maps, frequency-power spectra, Lyapunov exponents and fractal dimensions as chaotic measures. Period-doubling, sudden changes and intermittency bifurcations are observed.Part of this work was presented at the XVIIth Int. Congr. of Theor. and Appl. Mech., Grenoble, August 1988.