Propagation of thermoelastic waves across an interface with consideration of couple stress and second sound

Li, Yueqiu; Wei, Peijun; Wang, Changda

doi:10.1177/1081286517736999

Cited by 14 publications

(3 citation statements)

References 30 publications

(33 reference statements)

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“…It is found that for a two-dimensional model, there exist four coupled longitudinal waves, that is, longitudinal displacement wave, thermal wave, mass diffusion wave and longitudinal microstretch wave, as well as two coupled transverse waves. Considering the strain gradient theory and coupled stress theory, Li et al [45][46][47][48] further derived the governing equations of thermoelastic waves corresponding to the L-S, G-L and G-N generalized thermoelastic theories, and studied the dispersion and attenuation characteristics of thermoelastic waves, as well as the characteristics of reflection and transmission. It was found that the thermo-mechanical coupling effect only affects the longitudinal wave, not the shear wave.…”

Section: Introductionmentioning

confidence: 99%

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

Askes

Gitman

et al. 2023

Waves in Random and Complex Media

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A coupled thermoelastic model with fractional order derivative which incorporates the microstructural effects and thermoelastic coupling effects simultaneously at small scale is provided and is used to study wave dispersion and bandgap features of Bloch waves in one-dimensional phononic crystals. Dipolar gradient elasticity is used to account for the effects of microstructure while the non-Fourier heat conduction with fractional order derivatives is used to model thermal conduction at small scale. The interaction of thermoelastic coupled waves with a periodic structure leads to Bloch waves, and the transfer matrix method is used to obtain the dispersion equation of the Bloch waves based on the Bloch theorem. A parameter study is performed in the numerical example to investigate the influence of the strain gradient parameter, the micro-inertial parameter, the relaxation time and the fractional order on the dispersion and bandgap of Bloch waves.

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Section: Introductionmentioning

confidence: 99%

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

Askes

Gitman

et al. 2023

Waves in Random and Complex Media

Self Cite

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“…Biswas and Sarkar [32] found a solution of the oscillations equations in porous thermoelastic medium. Li et al [33] have examined the effects of couple stress on the propagation of thermoelastic waves. Saha et al [34] showed the effects of initial stresses and gravity field on the reflection and refraction coefficients of plane waves.…”

Section: Introductionmentioning

confidence: 99%

Transverse waves incident at the free surface of an initially stressed dissipative half-space

Selim¹,

Gepreel²

2021

Phys. Scr.

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In this work, an attempt is done to apply Biot`s incremental deformation theory to find out the effects of initial stresses on the reflected transverse waves (S-waves) at a free surface of dissipative half-space medium. Equations of motion and its corresponding solutions are derived in lights of Biot`s theory. The impact of initial stresses and medium`s dissipation on the reflected transverse wave are studied in detail. Numerical calculations carried out using Aswan geological crustal structure and the results are presented graphically. Numerical findings reveal that, the initial stresses and the medium dissipation effects the reflection coefficients of transverse wave considerably. In addition, it has been noted that, the phase velocity decreases considerably as the initial stress parameter increases. Since the crust of the Earth, , is dissipative and initially stressed medium, thus understanding the effects of these parameters may help seismologists to get accurate results of reflected seismic transverse wave at the surface of Earth crust.

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“…The reflection of longitudinal waves in non-dissipative medium including the effect of rotation was discussed by Sing et al [19]. More recently, Biswas and Sarkar [20] derived the solution of the steady oscillations equations in porous thermos-elastic medium and Li et al [21] discussed the propagation of thermos-elastic waves across an interface with consideration of couple stress and second sound on the basis of Green and Naghdi GN theories. Saha et al [22] analyzed the reflection and refraction of plane wave at the separating interface of two functionally graded incompressible monoclinic media under initial stress and gravity.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

Selim

Nofal

2020

Mathematics

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The aim of this work is to study the behavior of reflection of a longitudinal wave at a free surface of dissipative half-space under the effects of compressive initial stresses. When a longitudinal wave is incident on the free surface of an elastic dissipative half-space, two damped waves (Primarywaves and secondary waves are reflected. Among of these waves, P-waves are affected by compressional initial stresses. The governing equation and corresponding closed-form solutions are derived based on Biot’s incremental deformation theory. The equations of motion are solved analytically and the influence of initial stress parameter on the reflection coefficient of P-wave incidents at the free surface of dissipative half-space is studied in detail. Numerical computations are performed for actual Earth crust and the results analyzing the incident of longitudinal waves are discussed and presented graphically. The analytical solutions and numerical results reveal that the compressive initial stress parameter has notable effects on the reflection coefficient of longitudinal wave incidents on the free surface of dissipative medium. In addition, it has been observed that the presence of compressive initial stresses increases the phase velocity of the longitudinal waves. To the authors’ best knowledge, effects of compressive initial stresses on the reflection coefficients of the incident longitudinal wave on a free surface of dissipative half-space have not been studied before. Since the actual Earth is subject to initial stresses due to different resources, understanding the influences of compressive initial stresses on the reflection coefficient of a longitudinal wave helps seismologists and earthquake engineers to get accurate results of the reflection coefficients of seismic waves propagation in the Earth. Thus, the present study would be useful for seismology and earthquake engineering fields and further study about the nature of seismic waves.

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Propagation of thermoelastic waves across an interface with consideration of couple stress and second sound

Cited by 14 publications

References 30 publications

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

Band gaps of thermoelastic waves in 1D phononic crystal with fractional order generalized thermoelasticity and dipolar gradient elasticity

Transverse waves incident at the free surface of an initially stressed dissipative half-space

A Mathematical Model of Longitudinal Waves Incident at a Free Surface of a Pre-Stressed Dissipative Half-Space

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