Supercritical Nonlinear Dynamics of an Axially Moving Viscoelastic Beam with Speed Fluctuation

The present paper investigates the bifurcation and chaos of an axially moving viscoelastic beam in the supercritical transport speed ranges. The axially moving speed is assumed to be a small simple harmonic fluctuation about the constant mean speed. A dynamic model is established to include the finite axial support rigidity, the material derivative in the viscoelastic constitution relation, and the longitudinally varying tension due to the axial acceleration. Applying the Galerkin truncation method to the integro–partial–differential equation, the time histories are numerically solved for the axially moving viscoelastic beam. Based on the numerical solutions, the bifurcation diagrams are presented in the case that the amplitude of the speed fluctuation is varied while other parameters are fixed. For the first time, the nonlinear dynamics is compared with various terms Galerkin truncation, such as 2-term, 4-term, and 6-term. Numerical results show that the various terms Galerkin truncation can predict different nonlinear dynamic behavior of the supercritical axially moving viscoelastic beam