The dynamic behaviour of a finite railway under the high-speed multiple moving forces by using finite element method

Abstract

Based on the equivalence between the resonant frequency, the critical moving speed, the frequency spectrum and the maximum forced vibration response of the 'ÿnite' railway and those of the 'inÿnite' one, an inÿnite railway is replaced by a ÿnite one so that the ÿnite element method is available for the dynamic analysis of the 'ÿnite' railway subjected to the high-speed multiple moving forces. To agree with the practical situations, the dynamic behaviour of the 'discontinuous' railway is also investigated in addition to the traditional 'continuous' one. The in uence of the moving-load speed, the total number of moving loads and the spacing between any two adjacent moving loads on the dynamic behaviours of the continuous railway and the discontinuous railway is studied.

Analytical solutions for Euler–Bernoulli beam on visco‐elastic foundation subjected to moving load

“…The above equation is obtained following a similar procedure as that followed for Equations (30) and (31) with the assumptions that the horizontal ground displacements are negligible and that u z = we Àgz . Thus, the total mass per unit length r of the beam-soil system participating in the vibration is given by r = r b + r s .…”

“…Steele and Chen and Huang investigated the response of Timoshenko beam on Winkler foundation for a variety of beam, foundation and loading conditions. Finite‐element analyses, sometimes in conjunction with Fourier analysis, were also performed to investigate the response of different types of beams on Winkler foundations and on elastic half‐space considering homogeneous and heterogeneous soil properties .…”

Finite‐Element Formulae for Calculating the Sectional Forces of a Bernoulli‐Euler Beam on Continuously Viscoelastic Foundation Subjected to Concentrated Moving Loads

“…It is evident that the time histories with the finite element solution given by the revised proposed formula (11) are very close to those with the analytical solution given by Eq. (26). However, the difference between the time histories with the finite element solution given by the conventional formula (1) and those with the analytical solution given by Eq.…”

“…In the numerical methods, the finite element method (FEM) is powerful because it allows solution to complex problems in engineering. Some researchers [10,13,14,18,19,[23][24][25][26] applied FEM to study the foregoing dynamic problem. It is well known that in the design of a beam on elastic foundation or a simply supported beam subjected to moving loads, the most important considerations are the vertical deflection and the bending stress, and the latter is given by using bending moment divided by the section modulus of the beam.…”

“…It is well known that in the design of a beam on elastic foundation or a simply supported beam subjected to moving loads, the most important considerations are the vertical deflection and the bending stress, and the latter is given by using bending moment divided by the section modulus of the beam. References [14,18,23,25,26] did not care for the bending moment of beam. References [10,13,19,24] reported the bending moment of beam, but they did not give the formula to calculate the bending moment of beam.…”