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Waves in Inhomogeneous Solids

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Applied Wave Mathematics

Abstract

The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids. The basic governing equations are solved by means of a finite-volume scheme that is faithful, accurate, and conservative. Furthermore, this scheme is compatible with thermodynamics through the identification of the notions of numerical fluxes (a notion from numerics) and of excess quantities (a notion from irreversible thermodynamics). A selection of one-dimensional wave propagation problems is presented, the simulation of which exploits the designed numerical scheme. This selection of exemplary problems includes (i) waves in periodic media for weakly nonlinear waves with a typical formation of a wave train, (ii) linear waves in laminates with the competition of different length scales, (iii) nonlinear waves in laminates under an impact loading with a comparison with available experimental data, and (iv) waves in functionally graded materials.

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Authors and Affiliations

  1. Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, EE-12618, Tallinn, Estonia

    Arkadi Berezovski, Mihhail Berezovski & Jüri Engelbrecht

Authors
  1. Arkadi Berezovski
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  2. Mihhail Berezovski
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  3. Jüri Engelbrecht
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Correspondence to Arkadi Berezovski .

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Editors and Affiliations

  1. Tallinn University of Technology, Inst. Cybernetics, Estonian Academy of Sciences, Akadeemia Tee 21, Tallinn, 12618, Estonia

    Ewald Quak

  2. Tallinn University of Technology, Inst. Cybernetics, Estonian Academy of Sciences, Akadeemia Tee 21, Tallinn, 12618, Estonia

    Tarmo Soomere

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Berezovski, A., Berezovski, M., Engelbrecht, J. (2009). Waves in Inhomogeneous Solids. In: Quak, E., Soomere, T. (eds) Applied Wave Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00585-5_5

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