Continuum Mechanics and Thermodynamics

, Volume 29, Issue 6, pp 1219–1240 | Cite as

Dispersion relations for the hyperbolic thermal conductivity, thermoelasticity and thermoviscoelasticity

Original Article

Abstract

The Maxwell–Cattaneo heat conduction theory, the Lord–Shulman theory of thermoelasticity and a hyperbolic theory of thermoviscoelasticity are studied. The dispersion relations are analyzed in the case when a solution is represented in the form of an exponential function decreasing in time. Simple formulas that quite accurately approximate the dispersion curves are obtained. Based on the results of analysis of the dispersion relations, an experimental method of determination of the heat flux relaxation time is suggested.

Keywords

Hyperbolic thermoelasticity Hyperbolic thermoviscoelasticity Maxwell–Cattaneo law Heat flux relaxation Dispersion relations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Theoretical MechanicsPeter the Great Saint-Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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