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Acceleration waves and ellipticity in thermoelastic micropolar media

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Abstract

Acceleration waves in nonlinear thermoelastic micropolar media are considered. We establish the kinematic and dynamic compatibility relations for a singular surface of order 2 in the media. An analogy to the Fresnel–Hadamard–Duhem theorem and an expression for the acoustic tensor are derived. The condition for acceleration wave’s propagation is formulated as an algebraic spectral problem. It is shown that the condition coincides with the strong ellipticity of equilibrium equations. As an example, a quadratic form for the specific free energy is considered and the solutions of the corresponding spectral problem are presented.

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Authors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Zentrum für Ingenieurwissenschaften, Martin-Luther-Universität Halle-Wittenberg, 06099, Halle (Saale), Germany

    Holm Altenbach

  2. South Scientific Center of RASci and South Federal University, Milchakova st. 8a, 344090, Rostov on Don, Russia

    Victor A. Eremeyev

  3. Universidad Nacional de Colombia, Bogotá, Colombia

    Leonid P. Lebedev & Leonardo A. Rendón

Authors
  1. Holm Altenbach
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  2. Victor A. Eremeyev
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  3. Leonid P. Lebedev
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  4. Leonardo A. Rendón
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Correspondence to Holm Altenbach.

Additional information

The work was supported by the DAAD program “Forschungsaufenthalte für Hochschullehrer und Wissenschaftler” in 2008, by the Russian Foundation of Basic Research under grants 07-01-00525, and by Universidad Nacional de Colombia, project of investigation No. DIB 8003061.

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Altenbach, H., Eremeyev, V.A., Lebedev, L.P. et al. Acceleration waves and ellipticity in thermoelastic micropolar media. Arch Appl Mech 80, 217–227 (2010). https://doi.org/10.1007/s00419-009-0314-1

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