In this paper, a rail joint model consisting of three Euler-Bernoulli beams connected via a Winkler foundation is proposed in order to point out the influence of the joint gap length upon the stiffness of the rail joint. Starting from the experimental results aiming the stiffness of the rail joint, the Winkler foundation stiffness of the model has been calculated. Using the proposed model, it is shown that the stiffness of the rail joint of the 49 rail can decreases up to 10 % when the joint gap length increases from 0 to 20 mm.
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model is also used. It is worth remembering that in experimental studies, strain but not stress are measured. Hence, it follows that comparative theoretical and numerical studies should be conducted simultaneously for both gradient models. In this article, we study and compare two models of vibration of the Euler–Bernoullibeam under a moving force based on two different gradient versions of the nonlocal theory of elasticity, namely, the nonlocal Eringen’s model, in which the strain is a function of stress gradient, and the nonlocal Aifantis’s model, in which the
The contribution is mainly focused on research and development of structural modification of machine tools, lathes in particular. The main aim of the modification is to change the modal properties (mode shapes, natural frequencies) of the lathe tool. The main objective of the contribution will be to formulate, mathematical analyse and evaluate the proposed methods and procedures for structural modifications of the tool, represented by beam body. A modification of modal properties by insertion of beam cores into beam body is studied in this paper. In this paper, the effect of material properties and geometrical parameters of reinforcing cores on natural frequencies of beam body is presented. The implementation will bring benefit on machine productivity, decreasing the machine tool wear and in many cases it will lead to better conditions in the cutting process.
The paper is based on the analytical and experimental results from ,  and reveals, by mathematical methods, the degradation of ma- terial stifiness due to the decrease of the first natural frequency, when the driving frequency is slightly lower than the first natural frequency of the undegradated structure. By considering the vibration of the uni- form slender cantilever beam as an oscillating system with degrading hysteretic behavior the following equation is considered subjected to the boundary conditions To approximate the solution of the this problem, we use the method of Newton interpolating series (see ) and the Taylor series method (see ).
Euler-Bernoullibeam assumption and eigenvalue approach. The Laplace transform is applied to obtain the expressions for displacements, lateral deflection, temperature change, axial stress and chemical potential. The physical quantities are computed numerically and depicted graphically to show the effects of phase lags, Green-Naghdi (II) and Green-Naghdi (III) theories. 2 Basic Equations The constitutive relations, equations of motion, equation of heat conduction and equation of mass diffusion in a modified couple-stress generalized thermoelastic with mass diffusion in
Facilities, vol.422, pp.39-47.  Zhanga Guo-Dong and Guo Bao-Zhu (2011): On the spectrum of Euler-Bernoullibeam equation with Kelvin – Voigt damping. – Journal of Mathematical Analysis and Applications, vol.374, pp.347-358.  Beshliu V.A. (2012): Estimation of allowed gap value for welded rail rupture from the point of view of train safety. – Natural and Technical Risks. Constructions Safety, No.3, pp.56-58.  Zaitseva T.I. and Uzdin A.M. (2013): Estimation of safety for welded rail near seismic-isolated bridge. – Natural and Technical Risks. Constructions
). Differential evolution for multi-objective optimization, Proceedings of the 2003 Congress on Evolutionary Computation, CEC 2003, Canberra, Australia, pp. 2696-2703. Babu, B. and Munawar, S. (2007). Differential evolution strategies for optimal design of shell-and-tube heat exchangers, Chemical Engineering Science 62(14): 3720-3739. Bashash, S., Salehi-Khojin, A. and Jalili, N. (2008). Forced vibration analysis of flexible Euler-Bernoullibeams with geometrical discontinuities, Proceedings of the American Control Conference, ACC 2008, Seattle WA, USA, pp. 4029-4034. Biondi, B
Stabilization of One-Dimensional Anti-Stable Wave Equations Subject to Disturbance in Boundary Input. - IEEE Transactions on Automatic Control, Vol. 58, 2013, No 5, pp. 1269-1274. 10. Guo, B. Z., F. F. Jin. The Active Disturbance Rejection and Sliding Mode Control Approach to the Stabilization of Euler Euler-BernoulliBeam Equation with Boundary Input Disturbance. - Automatica, Vol. 49, 2013, No 9, pp. 2911-2918. 11. Liu, H., W. Gao. Study of the Feedforward Friction Compensation in Servo System. - Science Technology and Engineering, 2007, No 4, pp. 614-616 (in Chinese). 12
Developments, UK.  Idowu A.S. and Aguda E.V. (2012): Vibration analysis of Euler-Bernoullibeam with structural damping coefficient subjected to distributed moving load. - ICASTOR Journal of Mathematical Sciences, vol.6, No.1, pp.41-68. Published by Indian Centre for Advance Scientific and Technology, 91/1, Sybon Road, Rahara, Kolkata-700 118Available online www.icastorindia.in.  Cyril Touze, Ćedric Camier, Gael Favraud and Olivier Thomas (2008):́ Effect of imperfections and damping on the type of nonlinearity of circular plates and shallow spherical shells