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Journal ArticleDOI

Memory response in plane wave reflection in generalized magneto-thermoelasticity

22 Apr 2019-Journal of Electromagnetic Waves and Applications (Taylor & Francis)-Vol. 33, Iss: 10, pp 1354-1374
TL;DR: In this paper, the reflection phenomenon of the magneto-thermoelastic plane waves from a stress-free surface of a homogeneous, isotropic, thermally and electrically conducting solid half-space was demonstrated.
Abstract: This paper demonstrates the reflection phenomenon of the magneto-thermoelastic plane waves from a stress-free surface of a homogeneous, isotropic, thermally and electrically conducting solid half-space. We employ the generalized thermoelasticity model with memory-dependent derivative (MDD) for this study. We find that three basic plane waves consisting of two sets of coupled longitudinal waves and one independent shear type wave may travel with distinct speeds in the medium. The speeds of the coupled longitudinal waves are plotted graphically to predict a comparison for the MDD and Lord–Shulman models. At last, for an appropriate material, the reflection coefficients are computed numerically and presented graphically with the angle of incidence of the incident (vertically polarized) shear type wave and the obtained results are explained.
Citations
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Journal ArticleDOI
TL;DR: In this article, a new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address the reflection of thermo-elastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space.
Abstract: This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

10 citations

Journal ArticleDOI
TL;DR: In this article, the reflection of thermoelastic plane waves from the isothermal stress-free boundary of a homogeneous, isotropic and thermally conducting solid half-space was investigated.
Abstract: In this paper, we investigated the reflection of thermoelastic plane waves from the isothermal stress-free boundary of a homogeneous, isotropic and thermally conducting solid half-space in the cont...

7 citations


Cites background from "Memory response in plane wave refle..."

  • ...[31] studied thememory response in planewave reflection in generalizedmagneto-thermoelasticity....

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Journal ArticleDOI
TL;DR: In this paper, the effects of the kernel function, time-delay parameter, magnetic field and thermoelastic coupling parameter on the variations of different field quantities inside the half-space are analyzed graphically.

5 citations

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermo-elastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material.
Abstract: In the present manuscript, a two-dimensional generalized thermoelastic model is used to study the problem of reflection of thermoelastic plane waves from a stress-free and thermally insulated boundary of thermally conducting isotropic homogeneous elastic material. The Lord–Shulman model under the heat transfer law with memory-dependent derivative is employed to model this problem. The case of total reflection is taken into account to calculate the critical angle. Phase velocities and corresponding attenuation factors of the coupled dilatational elastic-thermal waves and the ratios of the reflection coefficients are calculated and illustrated graphically for copper-like material and highlighted the effects of various parameters of interest.

2 citations

Journal ArticleDOI
TL;DR: In this paper, the propagation of surface waves in generalized magneto-thermoelastic media under influence of magnetic field and rotation was studied and its applications in Engineering, Geophysics, and Medicine.
Abstract: This paper aims to study the propagation of surface waves in generalized magneto-thermoelastic media under influence of magnetic field and rotation and its applications in Engineering, Geophysics, ...

2 citations

References
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Book
01 Jan 1962
TL;DR: In this article, the linearized theory of elasticity was introduced and the elasticity of a one-dimensional motion of an elastic continuum was modeled as an unbound elastic continuum.
Abstract: Preface Introduction 1 One-dimensional motion of an elastic continuum 2 The linearized theory of elasticity 3 Elastodynamic theory 4 Elastic waves in an unbound medium 5 Plane harmonic waves in elastic half-spaces 6 Harmonic waves in waveguides 7 Forced motions of a half-space 8 Transient waves in layers and rods 9 Diffraction of waves by a slit 10 Thermal and viscoelastic effects, and effects of anisotrophy and non-linearity Author Index Subject Index

4,133 citations


Additional excerpts

  • ...The critical angle θC for the elastic case is given by θC = sin−1(β) [39]....

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Journal ArticleDOI
TL;DR: In this article, a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of heat flow.
Abstract: In this work a generalized dynamical theory of thermoelasticity is formulated using a form of the heat transport equation which includes the time needed for acceleration of the heat flow. The theory takes into account the coupling effect between temperature and strain rate, but the resulting coupled equations are both hyperbolic. Thus, the paradox of an infinite velocity of propagation, inherent in the existing coupled theory of thermoelasticity, is eliminated. A solution is obtained using the generalized theory which compares favourably with a known solution obtained using the conventional coupled theory.

3,266 citations


"Memory response in plane wave refle..." refers background or result in this paper

  • ...[22, 26] introduced the first order MDD, instead of fractional calculus, into the rate of heat flux in LS theory [4] of generalized thermoelasticity to denote memory-dependence as: ( 1 + τ0Dτ0 ) qi = −KT ,i,...

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  • ...The phase speeds of the coupled longitudinal waves are plotted graphically to predict a comparison between the MDD and the Lord–Shulman (LS) models....

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  • ...Lord and Shulman [4], Green and Lindsay [5], and Green and Naghdi [6] proposed three different generalized heat conduction equationswhich are themost discussed hyperbolic-type heat equations in the literature....

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  • ...This result agrees with that in the conventional coupled as well as LS theories [2, 4] of thermoelasticity....

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Journal ArticleDOI
TL;DR: In this article, a unified treatment of thermoelasticity by application and further developments of the methods of irreversible thermodynamics is presented, along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement.
Abstract: A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

2,287 citations


"Memory response in plane wave refle..." refers background or result in this paper

  • ...Initially, the motivation was to avoid the unpleasant feature of the classical coupled heat conduction model [2] in which the the thermal signals propagate with infinite speed....

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  • ...This result agrees with that in the conventional coupled as well as LS theories [2, 4] of thermoelasticity....

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Book
02 Dec 2010
TL;DR: In this paper, the existence and uniqueness results for Riemann-Liouville Fractional Differential Equations are presented. But they do not cover the special cases of fractional calculus.
Abstract: Fundamentals of Fractional Calculus.- Riemann-Liouville Differential and Integral Operators.- Caputo's Approach.- Mittag-Leffler Functions.- Theory of Fractional Differential Equations.- Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations.- Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results.- Single-Term Caputo Fractional Differential Equations: Advanced Results for Special Cases.- Multi-Term Caputo Fractional Differential Equations.

2,263 citations


"Memory response in plane wave refle..." refers methods in this paper

  • ...Diethelm [30] incorporated a kernel function and modified a Caputo-type fractional-order derivative as...

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Book
31 May 2010
TL;DR: The Eulerian Functions The Bessel Functions The Error Functions The Exponential Integral Functions The Mittag-Leffler Functions The Wright Functions as mentioned in this paper The Eulerians Functions
Abstract: Essentials of Fractional Calculus Essentials of Linear Viscoelasticity Fractional Viscoelastic Media Waves in Linear Viscoelastic Media: Dispersion and Dissipation Waves in Linear Viscoelastic Media: Asymptotic Methods Pulse Evolution in Fractional Viscoelastic Media The Eulerian Functions The Bessel Functions The Error Functions The Exponential Integral Functions The Mittag-Leffler Functions The Wright Functions.

1,593 citations