Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation

Babenkov, Mikhail B.

doi:10.1134/s0021894413020132

Cited by 13 publications

(1 citation statement)

References 4 publications

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“…[12][13][14] The speed of quasi-thermal and quasi-acoustic fronts of thermoelastic waves are summarized in the works. [12,14,15] The major work on different neoclassic theories of the thermoelasticity can be found in Jou, Casas-Vazquez and Lebon's book. [16] The detailed literature review on the hyperbolic thermoelasticity is presented in [17].…”

Section: Introductionmentioning

confidence: 99%

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

Matias

Vitokhin

2019

Z Angew Math Mech

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A numerical solution for a coupled hyperbolic thermoelasticity problem of the Lord-Shulman type is presented. An infinite layer with free boundaries that are kept at a constant temperature is irradiated by a short laser impulse. In this case the problem can be studied in the one-dimensional formulation. An impact of the laser impulse on a medium is modeled by an internal heat source. The laser impulse intensity decays with a distance from an irradiated surface according to the Bouguer law. The layer is in an unperturbed state at the initial moment of time. The material properties of copper are taken to be the thermo-mechanical properties of the layer.Two approaches for the boundary value problem are considered: the finite-difference method (FDM) and the finite-volume method (FVM). In the first case the system of two second-order PDE is investigated, in the second case a system of integral balance equations and an integral thermal conductivity equation are composed. To integrate these equations both the explicit and implicit schemes are used. The obtained results are compared with each other and with an analytical solution. A numerical error is estimated for different time and space step sizes. The features inherent in various ways of integration of the coupled hyperbolic thermoelastic problem with the thermal excitation are found. K E Y W O R D SEuler implicit scheme, explicit leap-frog scheme, finite-difference method, finite-volume method, tridiagonal matrix algorithm, Lord-Shulman hyperbolic thermoelasticity, Maxwell-Cattaneo equation, relaxation constant, trust region algorithm

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Section: Introductionmentioning

confidence: 99%

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

Matias

Vitokhin

2019

Z Angew Math Mech

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Nonlinear Thermal Elastic Diffusion Problems Applicable to Surface Modification

Knyazeva

Parfenova

2022

Lecture Notes in Mechanical Engineering

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Thermoelastic Waves in a Medium with Heat-Flux Relaxation

Babenkov

Vitokhin

2017

Encyclopedia of Continuum Mechanics

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Lord-Shulman thermoelasticity; Propagation of thermal elastic waves in a medium with heat-flux relaxation constant Definitions Thermoelastic waves are the solutions of the equations of coupled thermoelasticity. In the case of hyperbolic thermoelasticity, the solution is the sum of two traveling waves. The first terms are called quasithermal components, and the second terms are quasielastic components. These components of thermoelastic waves propagate in the medium with different velocities, dispersion, and attenuation rate.

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Propagation of harmonic perturbations in a thermoelastic medium with heat relaxation

Cited by 13 publications

References 4 publications

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

Nonlinear Thermal Elastic Diffusion Problems Applicable to Surface Modification

Thermoelastic Waves in a Medium with Heat-Flux Relaxation

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