Bifurcation and Strange Behavior for a Nonlinear Viscoelastic Rod System

Abstract

Longitudinal vibration of a nonlinear viscoelastic rod system with one end fixed and another end subjected to an axial periodical excitation was studied under the consideration of transverse inertia. By using Galerkin method, a combined Parametric and Forcing Excited cubic nonlinear dynamic system is derived for hard stiffness nonlinear material. Furthermore, arc-length technique is used for an accurate integral procedure, and numeric results are given detailedly. The process of the system evolved from stable periodic motion to chaos is illustrated in a period-doubling bifurcation graph in a parameter space, and the Lyapunov exponent spectrum is also given that is perfectly consistent with bifurcation process. The strange attractor obtained from Poincaré Map is present, which has different fractal dimension from Duffing’s one, so it may be a new chaotic attractor.