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Amplitude stochastic response of Rayleigh beams to randomly moving loads

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Abstract

We consider the problem of the nonlinear response of a Rayleigh beam to the passage of a train of forces moving with stochastic velocity. The Fourier transform and the theory of residues are used to estimate the mean square amplitude of the beam, while the stochastic averaging method gives the stationary probability density function of the oscillations amplitude. The analysis shows that the effect of the load random velocities is highly nonlinear, leading to a nonmonotonic behavior of the mean amplitude versus the intensity of the stochastic term and of the load weight. The analytic approach is also checked with numerical simulations. The effect of loads number on the system response is numerically investigated.

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Acknowledgements

G.F. acknowledges partial financial support from MIUR through PON R&C (Programma Operativo Nazionale “Ricerca e Competitività”) 2007–2013 under Grant No. PON NAFASSY, PONa3_00007. Part of this work was completed during a research visit of Prof Nana Nbendjo at the University of Kassel in Germany. He is grateful to the Alexander von Humboldt Foundation for financial support within the Georg Forster Fellowship.

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Authors and Affiliations

  1. Laboratory of Modelling and Simulation in Engineering,Biomimetics and Prototypes,Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    L. M. Anague Tabejieu, B. R. Nana Nbendjo & P. Woafo

  2. Department of Science and Technologies, University of Sannio, Via Port’ Arsa 11, 82100, Benevento, Italy

    G. Filatrella

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  1. L. M. Anague Tabejieu
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  2. B. R. Nana Nbendjo
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  3. G. Filatrella
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  4. P. Woafo
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Correspondence to B. R. Nana Nbendjo.

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Tabejieu, L.M.A., Nbendjo, B.R.N., Filatrella, G. et al. Amplitude stochastic response of Rayleigh beams to randomly moving loads. Nonlinear Dyn 89, 925–937 (2017). https://doi.org/10.1007/s11071-017-3492-3

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  • DOI: https://doi.org/10.1007/s11071-017-3492-3

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