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Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam

Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam
Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam
It is generally considered that a Timoshenko beam is superior to an Euler-Bernoulli beam for determining the dynamic response of beams at higher frequencies but that they are equivalent at low frequencies. Here, the case is considered of the parametric excitation caused by spatial variations in stiffness on a periodically supported beam such as a railway track excited by a moving load. It is shown that large differences exist between the results obtained using Timoshenko and Euler-Bernoulli beams for a railway track with typical parameters; the EulerBernoulli beam model underestimates this parametric excitation by around a factor of 3. This difference is shown to be due to shear deformation in the rail, which is significant for span lengths less than about 2 m. A 2.5D finite element model of the rail is used as a reference. This gives a deflection that is closer to the Timoshenko beam model. However, the displacement profile obtained from the Timoshenko beam model has a discontinuity of gradient at the support points, whereas neither the Euler-Bernoulli beam nor the 2.5D finite element model contains the discontinuity of gradient. Finally, the moving load is introduced explicitly in the various periodically supported models. The results for a moving constant load, expressed as an equivalent roughness, are not strongly affected by the load speed until the sleeper passing frequency approaches the vertical track resonance at which the track mass bounces on the support stiffness. Consequently, a quasi-static model gives satisfactory results for moderate load speeds.
2.5D finite element method, Euler-Bernoulli beam, Timoshenko beam, moving load, parametric excitation, periodically supported beam, railway track
0022-460X
Zhang, Xianying
2d0ba27f-b78b-4823-938f-fa42d6787ab5
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5
Sheng, Xiaozhen
84cceba0-fd8e-47a3-bff9-5847e8935201
Zhang, Xianying
2d0ba27f-b78b-4823-938f-fa42d6787ab5
Thompson, David
bca37fd3-d692-4779-b663-5916b01edae5
Sheng, Xiaozhen
84cceba0-fd8e-47a3-bff9-5847e8935201

Zhang, Xianying, Thompson, David and Sheng, Xiaozhen (2020) Differences between Euler-Bernoulli and Timoshenko beam formulations for calculating the effects of moving loads on a periodically supported beam. Journal of Sound and Vibration, 481, [115432]. (doi:10.1016/j.jsv.2020.115432).

Record type: Article

Abstract

It is generally considered that a Timoshenko beam is superior to an Euler-Bernoulli beam for determining the dynamic response of beams at higher frequencies but that they are equivalent at low frequencies. Here, the case is considered of the parametric excitation caused by spatial variations in stiffness on a periodically supported beam such as a railway track excited by a moving load. It is shown that large differences exist between the results obtained using Timoshenko and Euler-Bernoulli beams for a railway track with typical parameters; the EulerBernoulli beam model underestimates this parametric excitation by around a factor of 3. This difference is shown to be due to shear deformation in the rail, which is significant for span lengths less than about 2 m. A 2.5D finite element model of the rail is used as a reference. This gives a deflection that is closer to the Timoshenko beam model. However, the displacement profile obtained from the Timoshenko beam model has a discontinuity of gradient at the support points, whereas neither the Euler-Bernoulli beam nor the 2.5D finite element model contains the discontinuity of gradient. Finally, the moving load is introduced explicitly in the various periodically supported models. The results for a moving constant load, expressed as an equivalent roughness, are not strongly affected by the load speed until the sleeper passing frequency approaches the vertical track resonance at which the track mass bounces on the support stiffness. Consequently, a quasi-static model gives satisfactory results for moderate load speeds.

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Differences between Euler and Timoshenko beams for moving loadsFinal - Accepted Manuscript
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Accepted/In Press date: 1 May 2020
Published date: 1 September 2020
Additional Information: Funding Information: The work described here has been supported by the Ministry of Science and Technology of China under the National Key R&D Programme grant 2016YFE0205200 , ‘Joint research into key technologies for controlling noise and vibration of high-speed railways under extremely complicated conditions’, and the Engineering and Physical Sciences Research Council of the UK ( EPSRC ) under the programme grant EP/M025276/1 , ‘The science and analytical tools to design long life, low noise railway track systems (Track to the Future)’. All data published in this paper are openly available from the University of Southampton repository at https://doi.org/10.5258/SOTON/D1362 . Publisher Copyright: © 2020 Elsevier Ltd
Keywords: 2.5D finite element method, Euler-Bernoulli beam, Timoshenko beam, moving load, parametric excitation, periodically supported beam, railway track

Identifiers

Local EPrints ID: 441485
URI: http://eprints.soton.ac.uk/id/eprint/441485
ISSN: 0022-460X
PURE UUID: 0c13a0e0-36e2-4257-ba74-361e4ee1f425
ORCID for David Thompson: ORCID iD orcid.org/0000-0002-7964-5906

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Date deposited: 15 Jun 2020 16:31
Last modified: 23 Feb 2023 05:03

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Contributors

Author: Xianying Zhang
Author: David Thompson ORCID iD
Author: Xiaozhen Sheng

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