A Green-Naghdi Model in a 2D Problem of a Mode I Crack in an Isotropic Thermoelastic Plate

Abbas, Ibrahim A.; Alzahrani, Faris

doi:10.1134/s1029959918020017

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…The uniqueness of solution in the linear theory of thermoelasticity without energy dissipation proved by Chandrasekharaiahv . In several research works the GN theory without energy dissipation (TEWOED) was used to investigate the coupled generalized thermoelastic problems.…”

Section: Introductionmentioning

confidence: 99%

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

Das¹,

Sarkar

2019

Math Methods in App Sciences

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The generalized thermoelasticity theory based upon the Green and Naghdi model III of thermoelasticity as well as the Eringen's nonlocal elasticity model is used to study the propagation of harmonic plane waves in a nonlocal thermoelastic medium. We found two sets of coupled longitudinal waves, which are dispersive in nature and experience attenuation. In addition to the coupled waves, there also exists one independent vertically shear-type wave, which is dispersive but experiences no attenuation. All these waves are found to be influenced by the elastic nonlocality parameter. Furthermore, the shear-type wave is found to face a critical frequency, while the coupled longitudinal waves may face critical frequencies conditionally. The problem of reflection of the thermoelastic waves at the stress-free insulated and isothermal boundary of a homogeneous, isotropic nonlocal thermoelastic half-space has also been investigated. The formulae for various reflection coefficients and their respective energy ratios are determined in various cases. For a particular material, the effects of the angular frequency and the elastic nonlocal parameter have been shown on phase speeds and the attenuation coefficients of the propagating waves. The effect of the elastic nonlocality on the reflection coefficients and the energy ratios has been observed and depicted graphically. Finally, analysis of the various results has been interpreted. KEYWORDS dispersion, energy partition, nonlocal, thermoelasticity, phase speeds and attenuation, reflection MSC CLASSIFICATION 74J10; 73B18; 73D15; 35Q74 Math Meth Appl Sci. 2020;43:1313-1336.wileyonlinelibrary.com/journal/mma

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Section: Introductionmentioning

confidence: 99%

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

Das¹,

Sarkar

2019

Math Methods in App Sciences

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“…Das and Kanoria [22] also worked on magneto-thermo-elastic waves in a medium with infinite conductivity in the context of GN-III theory. Abbas and Alzahrani [23] studied Green-Naghdi Model in a 2D problem of a mode I crack in an Isotropic Thermoelastic Plate. Moreover Ezzat, El-Karamany and El-Bary [24] presented Two-temperature theory in Green-Naghdi thermoelasticity with fractional phase-lag heat transfer.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of magneto-thermo-elastic wave propagation in a finitely conducting medium under thermoelasticity of type I, II, III

Tiwari,

Mishra

2019

Preprint

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The present work is concerned with the propagation of electro-magneto-thermoelastic plane waves of assigned frequency in a homogeneous isotropic and finitely conducting elastic medium permeated by a primary uniform external magnetic field. We formulate our problem under the theory of Green and Naghdi of type-III (GN-III) to account for the interactions between the elastic, thermal as well as magnetic fields. A general dispersion relation for coupled waves is deduced to ascertain the nature of waves propagating through the medium. Perturbation technique has been employed to obtain the solution of dispersion relation for small thermo-elastic coupling parameter and identify three different types of waves. We specially analyze the nature of important wave components like, phase velocity, specific loss and penetration depth of all three modes of waves. We attempt to compute these wave components numerically to observe their variations with frequency. The effect of presence of magnetic field is analyzed. Comparative results under theories of type GN-I, II and III have been presented numerically in which we have found that the coupled thermoelastic waves are un-attenuated and nondispersive in case of Green-Naghdi-II model which is completely in contrast with the theories of type-I and type-III. Furthermore, the thermal mode wave is observed to propagate with finite phase velocity in case of GN-II model, whereas the phase velocity of thermal mode wave is found to be an increasing function of frequency in other two cases. We achieve significant variations among the results predicted by all three theories.

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Photothermal-induced interactions in a semiconductor solid with a cylindrical gap due to laser pulse duration using a fractional MGT heat conduction model

2023

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A Green-Naghdi Model in a 2D Problem of a Mode I Crack in an Isotropic Thermoelastic Plate

Cited by 5 publications

References 12 publications

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

Reflection of plane waves in generalized thermoelasticity of type III with nonlocal effect

A Comparative Study of magneto-thermo-elastic wave propagation in a finitely conducting medium under thermoelasticity of type I, II, III

Photothermal-induced interactions in a semiconductor solid with a cylindrical gap due to laser pulse duration using a fractional MGT heat conduction model

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