A simple finite element to consider the non-linear influence of the ballast on vibrations of railway bridges

This article proposes a new and simple finite element which can be used to analyze vertical vibrations in railway bridges. The main feature of the element is that the effect of the ballast is introduced through a non-linear longitudinal stiffness associated to the slip at the interface between the bridge and the ballast. Two numerical applications show that this element can be used to model the variation of the natural frequencies of the bridge as a function of the amplitude of vibration.