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Fractional thermoelasticity revisited with new definitions of fractional derivative
- Source :
- European Journal of Mechanics - A/Solids. 84:104043
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- Fractional thermoelastic models have been formulated from classical thermoelasticity or extended thermoelasticity, i.e. Lord-Shulman or Green-Naghdi theory. It seems different authors have different physical pictures on such topic, for instance, there exist several approaches from Lord-Shulman model to fractional order ones. This work is aimed to simplify the theoretical frameworks by clarifying connections between existed models. To this end, a new fractional thermoelasticity is established by directly extending classical thermoelasticity with the aids of new forms of fractional derivatives, i.e. Caputo-Fabrizio, Atangana–Baleanu and Tempered-Caputo definitions. All definitions are introduced into Fourier's law by a unified way with relaxation time incorporated. Theoretically, the present model may be simplified into existed fractional theory. Numerically, it has the capability of describing thermoelastic behaviors from fractional Lord-Shulman models. For numerical studies, Laplace transform method is adopted, and a two-layered structure subjected to thermal heating is considered, from which the effects of different fractional derivatives and relaxation time are firstly uncovered. And then, the influences of material constants of two layers, especially with interfacial conditions, are discussed in detail. Finally, some concluding remarks are made.
- Subjects :
- Work (thermodynamics)
Laplace transform
Mechanical Engineering
Structure (category theory)
General Physics and Astronomy
02 engineering and technology
021001 nanoscience & nanotechnology
Fractional calculus
symbols.namesake
020303 mechanical engineering & transports
Fourier transform
Thermoelastic damping
0203 mechanical engineering
Mechanics of Materials
symbols
Material constants
Applied mathematics
General Materials Science
0210 nano-technology
Mathematics
Subjects
Details
- ISSN :
- 09977538
- Volume :
- 84
- Database :
- OpenAIRE
- Journal :
- European Journal of Mechanics - A/Solids
- Accession number :
- edsair.doi...........bfb438a70120cb3a01e03c1c1503f9e4