A fast semi-analytical method for computing the response of railway tracks on nonlinear foundations
Résumé
The nonlinear vibration of railway tracks is a subject of some recent investigations. A main source of non-linearity comes from the railway foundations. For example, ballast and its lower layers or support systems of non-ballasted railway could have nonlinear behaviors. Models of beam under moving forces are often used for this dynamic system, and then the models are solved by numerical method or perturbation technique for some special nonlinear cases. This communication present a new method for calculating the response of railway tracks under moving trains loads. Based an analytical model of periodically supported beam, this model holds for all kinds of nonlinear foundations. Then, by using harmonic balance techniques and iteration procedures, a new method is developed to calculate the response of the model provided that the loading forces form a periodic impulse series. This kind of loading force represents charges of moving trains with equal mass wagons. This method is demonstrated to converge to the analytic solution of the model in case of linear foundation. Then, it is applied to bilinear and nonlinear foundation as examples. The results show that the nonlinear parameters of foundation have a strong influence on the railways track responses. This semi-analytical method is simple and could be efficient to compute the nonlinear vibrations of railway tracks.
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