“…We will use the latter equation to describe heat conduction, a possibility that has been previously exploited in several frameworks; in particular, it is worth mentioning the theory developed by Green and Naghdi, who introduced the procedure of postulating an entropy balance in [20] and proved in [22] the consistency of this approach with the one stemmed by the energy balance; 6 more recently, a similar issue has been discussed in [9,17].…”
Section: Extended Powers Internal and Externalmentioning
confidence: 99%
“…If we make borrow from [9,17] the small perturbation assumption ϑ o =θ o + θ(ζ, t), where θ is the small perturbation, the system (32) becomes:…”
Section: A First Example: Longitudinal Vibrationsmentioning
confidence: 99%
“…where (8.4), Section 8 in [35]). As for the dissipation ξ o , as in three-dimensional thermo-elasticity [23,24], we set…”
Section: A First Example: Longitudinal Vibrationsmentioning
We propose a model for thermo-elastic beams, consistent with the theory of linear threedimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating convenient a priori representations for mechanical and thermal displacements, the latter playing the role of an additional kinetic variable. Such representations are regarded as internal constraints, some involving the first, others the second gradient of deformation and thermal displacements; these constraints are maintained by reactive stresses and hyper-stresses of the type occurring in non-simple elastic materials of grade two, and by reactive entropy influxes and hyper-influxes.
“…We will use the latter equation to describe heat conduction, a possibility that has been previously exploited in several frameworks; in particular, it is worth mentioning the theory developed by Green and Naghdi, who introduced the procedure of postulating an entropy balance in [20] and proved in [22] the consistency of this approach with the one stemmed by the energy balance; 6 more recently, a similar issue has been discussed in [9,17].…”
Section: Extended Powers Internal and Externalmentioning
confidence: 99%
“…If we make borrow from [9,17] the small perturbation assumption ϑ o =θ o + θ(ζ, t), where θ is the small perturbation, the system (32) becomes:…”
Section: A First Example: Longitudinal Vibrationsmentioning
confidence: 99%
“…where (8.4), Section 8 in [35]). As for the dissipation ξ o , as in three-dimensional thermo-elasticity [23,24], we set…”
Section: A First Example: Longitudinal Vibrationsmentioning
We propose a model for thermo-elastic beams, consistent with the theory of linear threedimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating convenient a priori representations for mechanical and thermal displacements, the latter playing the role of an additional kinetic variable. Such representations are regarded as internal constraints, some involving the first, others the second gradient of deformation and thermal displacements; these constraints are maintained by reactive stresses and hyper-stresses of the type occurring in non-simple elastic materials of grade two, and by reactive entropy influxes and hyper-influxes.
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