Nonlinear Analysis of a Viscoelastic Beam Moving with Variable Axial Tension and Time-Dependent Speed

The nonlinear characteristics of a simply supported moving system have been investigated through the analytic-numeric approach under the joint influence of parametric and internal resonance. As the elongation set in the neutral layer is caused by the immobile end supports, the system exhibits geometric cubic nonlinearity. The moving velocity is assumed to vary harmonically over a mean value while the variable axial tension depends upon the parameters viz. velocity, support stiffness, and spatial coordinate. The analytical solution is carried out by the MMS technique directly attacking the higher-order partial differential equation of motion of the continua with end conditions. This leads to the generation of a set of complex variable modulation equations that control amplitude and phase modulation. The continuation algorithm is used to analyze the steady-state solutions to explore the impact of support stiffness, which still needs to be addressed in the existing literature. In addition, the influence of viscoelastic and viscous dampings has also been investigated. The outcomes of this study are unique and exciting, which may help in the design and operation of traveling systems.