Nonlinear models for transverse forced vibration of axially moving viscoelastic beams

Nonlinear models of transverse vibration of axially moving viscoelastic beams subjected external transverse loads via steadystate periodical response are numerically investigated. An integropartialdifferential equation and a partialdifferential equation of transverse motion can be derived respectively from a model of the coupled planar vibration for an axially moving beam. The finite difference scheme is developed to calculate steadystate response for the model of coupled planar and the two models of transverse motion under the simple support boundary. Numerical results indicate that the amplitude of the steadystate response for the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters and the integropartialdifferential equation gives results more closely to the coupled planar vibration.