A closed-form solution of beam on viscoelastic subgrade subjected to moving loads

A closed-form solution of beam on viscoelastic subgrade subjected to moving loads is proposed in this paper. The Greenʹs function of the beam is obtained by means of Fourier transform. Theory of linear partial differential equation is used to express the deflection of the beam in terms of the Greenʹs function. Beamʹs deflection is represented as a generalized integral using inverse Fourier transform. To evaluate this generalized integral analytically, poles of the integrand are identified using the theory of algebraic equation. Every pole and its order are isolated and given in a closed form. The theorem of residue is then applied to represent the generalized integral in the form of contour integral in the complex plane. Closed-form deflection and numerical computation of distinct cases are provided as an illustration of the proposed solution.