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Dynamics of a beam on a bilinear elastic foundation under harmonic moving load

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Abstract

The present paper is concerned with the numerical modelization of the transient dynamic response of a simply supported Euler–Bernoulli elastic beam resting on a Winkler-type foundation, under the action of a transverse concentrated load, moving at a constant velocity along the beam, displaying an harmonic-varying magnitude in time. The elastic foundation, assumed as homogeneous in space, behaves according to a bilinear constitutive law, characterized by two different stiffness coefficients in compression and in tension. A finite element method approach coupled with a direct integration algorithm is developed for efficiently tracing the nonlinear dynamic response of the beam-foundation system. An original automated procedure is set, as being apt to resolve all required space/time discretization issues. Extensive parametric numerical analyses are performed to investigate how the frequency of the harmonic moving load amplitude and the ratio between the foundation’s moduli in compression and in tension affect the so-called critical velocities of the moving load, leading to high transverse beam deflections. Analytical interpolating expressions are proposed and fitted for the achieved two-branch critical velocity trends. The present outcomes shall reveal potential practical implications in scenarios of contemporary railway engineering, especially in terms of lowering down the admissible high-speed train velocities, as for structural requirement or preventing potential passenger discomfort.

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Acknowledgements

The first two authors wish to acknowledge public research funding from “Fondi di Ricerca d’Ateneo ex 60%” and a ministerial doctoral grant and funds at the ISA Doctoral School, University of Bergamo, Department of Engineering and Applied Sciences (Dalmine).

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Authors and Affiliations

  1. Department of Engineering and Applied Sciences, University of Bergamo, viale G. Marconi 5, 24044, Dalmine (BG), Italy

    Diego Froio & Egidio Rizzi

  2. CERIS, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal

    Fernando M. F. Simões & António Pinto Da Costa

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  1. Diego Froio
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Froio, D., Rizzi, E., Simões, F.M.F. et al. Dynamics of a beam on a bilinear elastic foundation under harmonic moving load. Acta Mech 229, 4141–4165 (2018). https://doi.org/10.1007/s00707-018-2213-4

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