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Bernoulli–Euler beams with random field properties under random field loads: fractal and Hurst effects

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Abstract

Responses of Bernoulli–Euler beams with random field properties and also possibly under random field forcing are studied for random fields with linear, Matérn, Cauchy, and Dagum covariances. The latter two allow decoupling of the fractal dimension and Hurst effect. We find second-order characteristics of the beam displacement under various boundary conditions. In a number of cases, the results may be obtained in explicit analytical (albeit lengthy) forms, but as Cauchy and Dagum models are being introduced, one has to resort to numerics.

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Authors and Affiliations

  1. Department of Computational Mathematics, Capital Normal University, Beijing, China

    Lihua Shen

  2. Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Martin Ostoja-Starzewski

  3. Department of Mathematics, University Federico Santa Maria, 2360102, Valparaiso, Chile

    Emilio Porcu

Authors
  1. Lihua Shen
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  2. Martin Ostoja-Starzewski
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  3. Emilio Porcu
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Correspondence to Martin Ostoja-Starzewski.

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Shen, L., Ostoja-Starzewski, M. & Porcu, E. Bernoulli–Euler beams with random field properties under random field loads: fractal and Hurst effects. Arch Appl Mech 84, 1595–1626 (2014). https://doi.org/10.1007/s00419-014-0904-4

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  • DOI: https://doi.org/10.1007/s00419-014-0904-4

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