Abstract

International audience; The degradation of railway tracks can be observed through several measurement techniques. Recently, a method to diagnose the railway track using Fiber Bragg gratings (FBG) has been proposed. FBG are integrated inside the railway sleeper and is named a "Smart Sleeper". To study the sleeper behavior, an analytical model for the dynamics of railway sleepers has been developed, which can calculate rapidly the sleeper responses. In this model, by using the relation between the rail forces and displacements of a periodically supported beam, the dynamic equation of the sleeper is written with the help of the Euler-Bernoulli beam equation and Dirac's functions. Subsequently, thanks to the Green's function of this system, the sleeper dynamic response is calculated analytically. A linear relation between the train loads and the sleeper strains is shown in the frequency domain. This article presents an application of this model to calculate the train loads from the strains measured by the FBG. Based on the analytical model, we obtain a matrix which presents the link between the loads and the sleeper responses. By integrating this matrix and the Fourier transform of the measurements recorded by the FBG at the middle and at the two rail-seats, the train loads can be quickly calculated by using the solver mldivide of MATLAB. The numerical application shows that the identified train loads are different for different wheels and different rails. This highlights the irregularity of the wheel-rail contact forces which can be used to detect the defaults in the rolling stock in future works.

Abstract

We study unsteady elastic diffusion vibrations of a freely supported rectangular isotropic Kirchhoff-Love plate on an elastic foundation, which is under the action of a distributed transverse load. A model that describes coupled elastic diffusion processes in multicomponent continuum is used for the mathematical problem formulation. The longitudinal and transverse vibrations equations of a rectangular isotropic Kirchhoff-Love plate with diffusion were obtained from the model using the d'Alembert variational principle. The problem solution of unsteady elastic diffusion plate vibrations is sought in integral form. The bulk Green's functions are the kernels of the integral representations. To find the Green's functions, we used the Laplace transform in time and the expansion into double trigonometric Fourier series in spatial coordinates. Green's functions in the image domain are represented in the form of rational functions depends on the Laplace transform parameter. The transition to the original domain is done analytically through residues and tables of operational calculus. The bulk Green's functions analytical expressions are obtained. Using a two-component continuum, a numerical study of unsteady mechanical and diffusion fields interaction is done for an isotropic plate. The solution is presented in analytical form, as well as in the form of three-dimensional graphs of the displacement fields and concentration increments on time and coordinates.

Abstract

We investigated unsteady elastic diffusion vibrations of a rectangular isotropic Timoshenko plate. For the mathematical problem formulation, a model of coupled elastic diffusion processes in a multicomponent continuum is used. Using the d'Alembert variational principle, the equations of transverse vibrations of a rectangular isotropic Timoshenko plate taking into account diffusion are obtained from this model. An initialboundary value problem of a simply supported plate bending is formulated.