Mathematical Analysis of Shearing Viscoelastic Beam Subjected to Continuous Moving Load

Abstract

In this paper, the dynamic response of a viscoelastic beam subjected to a moving distributed load has been studied. The viscoelastic properties of the beam have been considered as linear standard model in shear and incompressible in bulk. The stress components have been separated to the shear and dilatation components and as a result the governing equations in viscoelastic form has been obtained using direct method. These equations have been solved by the eigenfunction expansion method. In this research, according to the introduced dimensionless coefficients, a parametric study has been presented and the effects of the load velocity and viscoelastic materials have been investigated. The obtained results show the maximum decay corresponds to the cases that the first natural period equals totimes that the relaxation time.