Dynamic Response of an Axially Moving Viscoelastic Timoshenko Beam

In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The method of multiple scales with the solvability condition is applied to dimensionless form of  governing equations in modal analysis and principal parametric resonance. By a parametric study, the effects of velocity, geometry and­ ­viscoelastic­ parameters are investigated on the response.