AN EXAMINATION OF CHAOTIC MOTION FOR THE BUCKLED BEAM (DYNAMICS

In this thesis, the dynamics of a magnetically buckled beam are analyzed in detail, with a particular slant towards determining why the system exhibits chaotic behavior. The system behavior is analyzed by considering both an experimental and theoretical model. The theoretical model consists of a Rayleigh-Ritz modal expansion. For this theoretical model, chaos boundaries in the parameter space are mapped. Time histories and Poincare maps are calculated. Initial condition maps of different types are also generated. Lyapunov exponents are calculated for one, two and three mode approximations to the partial differential equation describing the motion. In the experimental analysis, power spectra are calculated from experimentally recorded time histories. Lyapunov exponents are also calculated from these experimental time histories and compared with the theoretical work.;Major results from this dissertation include a verification of the accuracy of the theoretical model for predicting physical behavior. The initial condition maps demonstrate fractal behavior, giving an insight into why chaotic motion occurs. The Lyapunov exponents generated from the theoretical modal expansions were also shown to converge. Since the Lyapunov exponents give a quantitative value to modal activity, it is now possible to determine the amount each mode contributes to system behavior. The Lyapunov exponents calculated from the experimentally obtained time histories compared well with the theoretical values. The power spectra obtained from experimental time histories also compared well with power spectra calculated from the modal expansion.