Abstract:

Forced vibration is numerically investigated for planar vibration of axially moving viscoelastic beams with simple supports. The material time derivative is used in the viscoelastic constitutive relation for the governing equation.It is assumed that excitation is spatially uniform and temporally harmonic. A finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate that there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies.Numerical results also indicate that amplitudes of stable steady-state responses decrease with the viscosity coefficient and the nonlinear coefficient, and increase with the amplitude of excitation.

Key words: axially moving beam; viscoelasticity; vibration; nonlinear; stability; finite difference