Multiple Stability and Unpredictable Outcomes in the Chaotic Vibrations of Euler Beams

Abstract

Nonlinear phenomena in the vibration of a slender, Euler-Bernoulli beam in compression and under periodic transverse loading is investigated. A feature of this system is the coexistence of distinct bifurcation branches which provide a rich resource for numerous solution states. An indepth study based on an energy approach is done to illustrate the presence of multiple stability resulting from the multiplicity of resonant solutions. Although the behaviors may exhibit a variety of different motions, the ultimate state is very sensitively dependent upon the initial conditions. The structures of boundary basins for the coexisting attractors are illustrated and the unpredictability of outcome is discussed in detail.