Periodic and chaotic motions of an unsymmetrical oscillator in nonlinear structural dynamics

The chaotic dynamics of a harmonically-excited single-degree-of-freedom unsymmetric system in continuum nonlinear structural dynamics is studied in some detail through computer simulations. The quadratic and cubic nonlinearities occurring in the motion equation model the geometrical and mechanical characteristics of a suspended elastic cable vibrating in its plane and actually exhibiting a single equilibrium position. Regions of different periodic or chaotic responses in the forcing control parameter space are obtained. Three main frequency ranges are distinguished, two located in the neighbourhood of the order one-half and one-third subharmonic resonances of the system, the third one covering the zones of order three and two superharmonic resonances. Several types of bifurcations and strange attractors are observed and identified through various dynamic measures, both qualitative and quantitative. The algorithmic experience about their use in situations with different “chaoticity” is augmented.