Selection of the Span Length of an Analogic Finite Beam to Simulate the Infinite Beam Resting on Viscoelastic Foundation Under a Harmonic Moving Load

Abstract

Continuous rails are often modeled as infinite beams. In this paper, closed-form solution is newly derived by the residue theorem and Green’s function for the dynamic response of an infinite beam resting on viscoelastic foundation under a harmonic moving load. The most suitable span length will be determined for the analogic finite beam (which can be more conveniently used in practice) to best represent the deflection of the infinite beam for practical reasons. Starting from the equations of motion, closed-form solution is firstly derived for the infinite beam. Then, it is verified by the finite element method (FEM) using semi-infinite elements to simulate the infinite boundary conditions. The deflection curves of the infinite beam and analogic finite beam are compared for various parameters. It is concluded that: (1) a larger span length should be adopted for the finite beam under higher load speeds or with foundations of softer stiffness or larger damping; typically, for load speeds [Formula: see text][Formula: see text]m/s (324[Formula: see text]km/h); (2) typically, a span length of 50 m can be adopted for the analogic beam for UIC rails resting on foundations with stiffness [Formula: see text] and damping coefficient [Formula: see text]; (3) the peak deflection of the infinite and analogic finite beams occurs after the moving load for foundations with larger damping; and (4) the shape and amplitude of the deflection curve vary as the load frequency and amplitude varies, but the difference between the two beams is insignificant for moving loads with high frequencies.