Transition From Soliton to Chaotic Motion Following Sudden Excitation of a Nonlinear Structure

Abstract

The existence of a transition from soliton-like motions to spatially and temporally disordered motions in a periodic structure with buckling nonlinearity is demonstrated. An experiment consisting of nine harmonic oscillators coupled with buckling sensitive elastica was constructed. This experiment is modeled using a modified Toda lattice. As has been shown in previous work, the experiment and the model show strong sensitivity to initial conditions. Here we show that this sensitivity may be related to a transition from relatively ordered solitary wave motion, immediately following the impact, to disordered motions at a later time. Some of the behavior of the observed wave structures is explained using Toda’s analytical results; however, the reasons for the break-up of the waves and their role in the generation of spatio-temporal disorder is not fully understood. We speculate that some type of transient chaotic motion is responsible for the observed behavior. These findings are relevant to aircraft, ship, and space structures that are subjected to large dynamic loads.