The mechanical characteristics of the railway superstructure are related to the properties of the ballast, and especially to the particle size distribution of its grains. Under the constant stress-strain of carriages, the ballast can deteriorate over time, and consequently it should properly be monitored for safety reasons. The equipment which currently monitors the railway superstructure (like the Italian diagnostic train Archimede) do not make any “quantitative” evaluation of the ballast. The aim of this paper is therefore to propose a new methodology for extracting railway ballast particle size distribution by means of the image processing technique. The procedure has been tested on a regularly operating Italian railway line and the results have been compared with those obtained from laboratory experiments, thus assessing how effective is the methodology which could potentially be implemented also in diagnostic trains in the near future.

On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Karman type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the power-law and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.