### Abstract

In this paper, an extended formula for the critical velocity of a uniformly moving load is derived. It is assumed that the load is traversing an infinite beam supported by finite depth foundation under plane strain condition. The critical velocity is extracted by parametric analysis applied on the analytical solution of the steady state deflection beam shape. Results obtained are compared with the previously published results of this author, where simplified assumptions were implemented on the shear contribution. It is confirmed that there is an interaction between the beam and the foundation and thus the critical velocity is dependent on the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass. Several options for damping are also analysed and results of displacement fields are compared with finite element simulations. In order to obtain steady-state form of the finite element results, the enhanced moving widow method is implemented in software ANSYS.

Original language | English |
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Title of host publication | ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering |

Publisher | National Technical University of Athens |

Pages | 4520-4527 |

Number of pages | 8 |

Volume | 3 |

ISBN (Electronic) | 978-618828440-1 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

Event | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 - Crete, Greece Duration: 5 Jun 2016 → 10 Jun 2016 |

### Conference

Conference | 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016 |
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Country | Greece |

City | Crete |

Period | 5/06/16 → 10/06/16 |

### Fingerprint

### Keywords

- Analytical solution
- Critical velocity
- Finite soil depth
- Integral transforms
- Moving load
- Moving window method

### Cite this

*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering*(Vol. 3, pp. 4520-4527). National Technical University of Athens. https://doi.org/10.7712/100016.2129.11208

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*ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering.*vol. 3, National Technical University of Athens, pp. 4520-4527, 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, Crete, Greece, 5/06/16. https://doi.org/10.7712/100016.2129.11208

**Extended formula for the critical velocity of a load moving on a beam supported by a finite depth foundation.** / Dimitrovová, Zuzana.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Extended formula for the critical velocity of a load moving on a beam supported by a finite depth foundation

AU - Dimitrovová, Zuzana

N1 - FCT, through IDMEC, under LAETA, project UID/EMS/50022/2013.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - In this paper, an extended formula for the critical velocity of a uniformly moving load is derived. It is assumed that the load is traversing an infinite beam supported by finite depth foundation under plane strain condition. The critical velocity is extracted by parametric analysis applied on the analytical solution of the steady state deflection beam shape. Results obtained are compared with the previously published results of this author, where simplified assumptions were implemented on the shear contribution. It is confirmed that there is an interaction between the beam and the foundation and thus the critical velocity is dependent on the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass. Several options for damping are also analysed and results of displacement fields are compared with finite element simulations. In order to obtain steady-state form of the finite element results, the enhanced moving widow method is implemented in software ANSYS.

AB - In this paper, an extended formula for the critical velocity of a uniformly moving load is derived. It is assumed that the load is traversing an infinite beam supported by finite depth foundation under plane strain condition. The critical velocity is extracted by parametric analysis applied on the analytical solution of the steady state deflection beam shape. Results obtained are compared with the previously published results of this author, where simplified assumptions were implemented on the shear contribution. It is confirmed that there is an interaction between the beam and the foundation and thus the critical velocity is dependent on the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass. Several options for damping are also analysed and results of displacement fields are compared with finite element simulations. In order to obtain steady-state form of the finite element results, the enhanced moving widow method is implemented in software ANSYS.

KW - Analytical solution

KW - Critical velocity

KW - Finite soil depth

KW - Integral transforms

KW - Moving load

KW - Moving window method

UR - http://www.scopus.com/inward/record.url?scp=84995530425&partnerID=8YFLogxK

U2 - 10.7712/100016.2129.11208

DO - 10.7712/100016.2129.11208

M3 - Conference contribution

VL - 3

SP - 4520

EP - 4527

BT - ECCOMAS Congress 2016 - Proceedings of the 7th European Congress on Computational Methods in Applied Sciences and Engineering

PB - National Technical University of Athens

ER -