Nonlinear dynamical behaviors of an axially moving viscoelastic beam

In this paper, the nonlinear dynamic behaviors of an axially moving viscoelastic beam with one-to-two internal resonance are investigated. Firstly, we utilize Hamilton's principle to derive the governing equations of motion for an axially moving viscoelastic beam with the integral constitution relations. Then, the Galerkin's approach is applied directly to the partial differential governing equation of motion to obtain a set of ordinary differential equations. Based on the case of 1:2 internal resonances, we can obtain averaged equations by using the method of multiple scales. Finally, numerical simulation is performed to study the three dimensional phase portraits of the axially moving viscoelastic beam. From the results of numerical simulation, it is found that there exist the periodic and chaotic motions in the axially moving viscoelastic beam system under certain conditions.