DYNAMICAL SYSTEM ANALYSIS FROM NONLINEAR TRANSITION TO CHAOS FOR A CRACKED PLATE

Abstract

Nonlinear vibrations for an isotropic cracked plate with different possible boundary conditions subjected to transverse harmonic excitation are evaluated. The first mode is examined in detail around the resonant region. A crack consisting of a continuous line is arbitrarily located at the middle and along the x-axis of the plate. The nonlinear dynamical systems analysis of this cracked plate model begins with the stability of the phase states, and the Poincare map followed by a study of the bifurcations that are observed from the analysis of saddle trajectories, and the estimation of the Lyapunov exponent. This leads to the emergence of strange attractors of fractal dimension, the evolution of saddle orbits into chaos, and to the observation that in this system seemingly chaotic behaviour can emerge from perfectly deterministic origins. In this study, the computational methods required are implementations of the Dynamics 2 software package, and specialized code written in Mathematical. Results shows that the system response could be extremely susceptible to changes in the control parameters, and the variation in the half crack length at the plate centre is one influence on the system s bifurcation and chaos.