### MODELLING THE VIBRATORY EFFECTS OF RAIL TRAFFIC ON THE ENVIRONMENT

Valeriu IONICĂ, Nicolae DUMITRU, Ionuț GEONEA, Mihaela BOGDAN

#### Abstract

Despite numerous technological advances, noise and the various forms it takes is perceived as a multiple source of environmental problems that are increasingly borne by humans. Sensitivity to rail traffic vibrations is the most important issue in the opinion of researchers. In this paper is determined the dynamic vibration response of the vehicle-railway system.  For this purpose, the most modern integration methods used for such purposes at present are used. For the two-degree-of-freedom, unloaded model for the railway, it is used the one-sided Laplace transform with respect to time that led to the algebraization of the problem, which simplified the integration of the differential equation system. With the Mathematica program, based on the numerical data presented in the paper, we inverted the Laplace transforms, resulting in the displacements as time functions, and then, with the same program, we obtained the graphical representations of the rail displacements caused by its geometrical imperfections. Next, using the same method, we obtained graphical representations of the bogie and wheel displacements caused by forced and damped vibrations induced in the system by the action of a force. For the determination of the deflection of the flexible rail track under a moving load the mathematical model is a partial derivative equation. We integrated this mathematical model by first applying the one-sided Laplace transform with respect to time, resulting in a Laplace image equation, to which we applied the finite sine Fourier transform. Solving the resulting algebraic system, we obtained the dynamic response of the mechanical system in Laplace and Fourier images. Applying first the inverse of the Laplace transform and then the inverse of the Fourier transformation in sine to the algebraic system, we obtained the solution of the partial derivative equation mentioned above in the form of a time and displacement function, which we plotted with the Mathematica program.

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