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Thermoelasticity with Finite Wave Speeds$
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Józef Ignaczak and Martin Ostoja-Starzewski

Print publication date: 2009

Print ISBN-13: 9780199541645

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199541645.001.0001

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Physical Aspects and Applications of Hyperbolic Thermoelasticity

Physical Aspects and Applications of Hyperbolic Thermoelasticity

Chapter:
(p.321) 12 Physical Aspects and Applications of Hyperbolic Thermoelasticity
Source:
Thermoelasticity with Finite Wave Speeds
Author(s):

Józef Ignaczak

Martin Ostoja‐Starzewski

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199541645.003.0012

This chapter first provides a brief review of several other theories, all classified as generalized thermoelasticity and due to Green and Naghdi. Next follows a justification of the presence of a material time derivative rather than a partial time derivative in the Maxwell‐Cattaneo equation. Another way to see this is to take the continuum thermodynamics as a starting point for the derivation of constitutive laws. However, the partial time derivative may be employed in a theory focused on solid mechanics in infinitesimal strains. In the sequel, some applications of the L‐S and G‐L theories are given: helices and chiral media, both with homogeneous as well as composite structures; surface waves; and thermoelastic damping in nanomechanical resonators. The chapter culminates with a thermoelasticity with anomalous heat conduction treated via fractional calculus, and a formulation of thermoelasticity of fractal media in the vein of dimensional regularization.

Keywords:   generalized thermoelasticity, Maxwell‐Cattaneo equation, continuum thermodynamics, helix, chiral media, surface waves, thermoelastic damping, resonators, fractional calculus, anomalous heat conduction, fractal media

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