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On the thermodynamically consistent fractional wave equation for viscoelastic solids

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Abstract

Since the well-known methods for the computation of harmonically induced LAMB waves in elastic plates cannot be applied directly to viscoelastic material, an enhanced material model is developed. It is based on fractional time derivatives and incorporates a fractional KELVIN–VOIGT model. A proof of the thermodynamic consistency of this model is given. On the basis of the developed material model, the fractional wave equation is derived which allows for the calculation of LAMB waves in viscoelastic solids.

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Authors and Affiliations

  1. Rolls-Royce Deutschland Ltd & Co KG, Eschenweg 11, Dahlewitz, 15827, Blankenfelde-Mahlow, Germany

    Sven von Ende

  2. Institute of Mechanics, University of the Federal Armed Forces Munich, 85577, Neubiberg, Germany

    Alexander Lion

  3. Institute of Mechanics, Helmut-Schmidt-University / University of the Federal Armed Forces Hamburg, 22043, Hamburg, Germany

    Rolf Lammering

Authors
  1. Sven von Ende
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  2. Alexander Lion
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  3. Rolf Lammering
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Correspondence to Sven von Ende.

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von Ende, S., Lion, A. & Lammering, R. On the thermodynamically consistent fractional wave equation for viscoelastic solids. Acta Mech 221, 1–10 (2011). https://doi.org/10.1007/s00707-011-0484-0

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  • DOI: https://doi.org/10.1007/s00707-011-0484-0

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