Vibrational study of nonlinear euler beam

Abstract

The chaotic vibrations of a simply supported slender beam is studied based on Euler Bernoulli theory. The partial differential equation is normalized and Galerkin procedure applied. Through forth order Runge Kutta numerical method, the vibratory effects are simulated. The resulting state responses, bifurcation branch diagrams, Poincare maps and boundary basins are studied. The unpredictability of the outcome is discussed in details as the boundary basin evolves under increasing driving force. More specifically, eight basins of attraction are obtained under the simulated conditions. The patterns from these eight attractors under different initial conditions are exhibited to show how changes in initial conditions can result in drastically different response.