Fractional Cattaneo-Type Equations and Generalized Thermoelasticity
- 11 January 2011
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Thermal Stresses
- Vol. 34 (2), 97-114
- https://doi.org/10.1080/01495739.2010.511931
Abstract
Following Compte and Metzler, the generalized Cattaneo-type equations with time-fractional derivatives are considered. The corresponding theory of thermal stresses is formulated. The proposed theory, on the one hand, interpolates the theory of Lord and Shulman and thermoelasticity without energy dissipation of Green and Naghdi and, on the other hand, generalizes theory of thermal stresses based on the fractional heat conduction equation. The fundamental solution to the nonhomogeneous fractional telegraph equation as well as the corresponding stresses are obtained in one-dimensional and axisymmetric cases.Keywords
This publication has 18 references indexed in Scilit:
- Time Fractional Diffusion: A Discrete Random Walk ApproachNonlinear Dynamics, 2002
- Nonclassical dynamical thermoelasticityInternational Journal of Solids and Structures, 2000
- GENERALIZED THERMOELASTICITYJournal of Thermal Stresses, 1999
- Hyperbolic Thermoelasticity: A Review of Recent LiteratureApplied Mechanics Reviews, 1998
- MACROSCALE AND MICROSCALE THERMAL TRANSPORT AND THERMO-MECHANICAL INTERACTIONS: SOME NOTEWORTHY PERSPECTIVESJournal of Thermal Stresses, 1998
- Thermoelasticity without energy dissipationJournal of Elasticity, 1993
- Thermoelasticity with Second Sound: A ReviewApplied Mechanics Reviews, 1986
- On the Theory of Relaxation for Systems with “Remnant” MemoryPhysica Status Solidi (b), 1984
- To the Theoretical Explanation of the “Universal Response”Physica Status Solidi (b), 1984
- A general theory of heat conduction with finite wave speedsArchive for Rational Mechanics and Analysis, 1968