Two-Dimensional Nonlinear Dynamics of Axially Accelerating Beam Based on DQM

In this paper, the two-dimensional nonlinear dynamics are investigated for the nonplanar nonlinear vibrations of an axially accelerating moving viscoelastic beam with in-plane and out-of-plane vibrations by the differential quadrature method (DQM). The coupled nonlinear partial differential equations for the two-dimensional nonplanar nonlinear vibrations are discretized in space and time domains using DQ and Runge-Kutta-Fehlberg methods respectively. Based on the numerical solutions, the nonlinear dynamical behaviors such as bifurcations and chaotic motions of the nonlinear system are investigated by use of the Poincare map, the three-dimensional phase portrait and the bifurcation diagrams. The bifurcation diagrams for the in-plane and out-of-plane displacements via the mean axial velocity and the amplitude of velocity fluctuation are respectively presented while other parameters are fixed.