Nonlinear vibration of axially moving materials: some new progresses

Some latest progress in the investigations on nonlinear vibration of axially moving materials were presented. The governing equations of axially moving materials were derived from the equations of the stationary counterparts via the transformation of coordinates. Two nonlinear models of transverse vibration of axially moving strings were numerically investigated by contrasting the responses calculated based on two models with those of the coupled equations of in-plan motion. The solvability condition was proposed in the general framework of the multi-scale analysis on a linear gyroscopic continuous system under the condition of small nonlinear time-dependent disturbances. Energetics of axially moving strings was treated to demonstrate that the energy is not conserved for a string moving in a constant axial speed and constrained by two fixed ends, and a conserved quantity is defined.