On the vertical effect of the Non-linear behavior of track–bridge interaction in simply supported railway bridges

Abstract

The present paper is devoted to studying the influence of the nonlinear behavior of the ballasted track on the dynamic response of a simply supported, non-skewed single ballasted track railway bridge acted by moving trains at constant speeds. Based on a double-beam model the rail track and the bridge deck are modeled as a simply supported Euler–Bernoulli upper beam and lower beam, respectively, which are connected between them through a vertical nonlinear continuous layer with viscous damping, which schematizes the mechanism of the vertical track–bridge interaction. The moving trains are modeled as a series of moving vertical forces (Moving Load Model). The nonlinear viscoelastic layer model describing the behavior of the rail bed is assumed to be a cubic-plus-bilinear type foundation; in particular, a bilinear constitutive law is introduced by the fact that this connection layer is characterized by two stiffness coefficients in compression and in tension at vertical zero deflection. The nonlinear partial differential equations that govern the transverse motion of the coupled system are determined. The Galerkin method and the fourth-order Runge–Kutta method are used to discretize and determine numerically the time–history response of the considered bridge. The obtained numerical results at the first order have shown that the dynamics of the coupled ballasted track–bridge system is governed by a Duffing like oscillator. The effect of the nonlinear behavior of the ballasted track cannot be neglected and yields decreased critical speeds and decreasing resonant amplitudes.