Fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model

Biswas, Siddhartha; Sarkar, Nantu

doi:10.1016/j.mechmat.2018.08.008

Cited by 44 publications

(17 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The reflection of plane waves in thermoelastic microstructured materials under the influence of gravitation in the context of Green‐Naghdi theory was reported by Abo‐Dahab . More recently, Biswas and Sarkar derived the solution of the steady oscillations equations in porous thermoelastic medium.…”

Section: Introductionmentioning

confidence: 91%

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

Das¹,

Sarkar

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Introductionmentioning

confidence: 91%

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

Das¹,

Sarkar

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…[17–19] studied the reflection of plane waves from electro‐magneto‐thermoelastic half‐space with a dual‐phase‐lag model. Biswas and Sarkar [20] derived the solution of the steady oscillations equations in a porous thermoelastic medium. Li et al.…”

Section: Introductionmentioning

confidence: 99%

“…They also discussed the reflection phenomena of P‐wave from a stress‐free solid half‐space. Biswas and Sarkar [20] derived the solution of the steady oscillations equations in porous thermoelastic medium with the dual‐phase‐lag model. They also studied the phase velocity, attenuation coefficient and penetration depth of time‐harmonic plane waves in a porous thermoelastic medium with dual‐phase‐lag.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

Sarkar

Mondal²

2020

Z Angew Math Mech

Self Cite

View full text Add to dashboard Cite

The present study is concerned with the reflection and propagation of thermoelastic plane waves from the stress‐free and thermally insulated surface of a homogeneous, isotropic thermally conducting elastic half‐space in the frame of modified Green–Lindsay theory of generalized thermoelasticity with two‐temperature (2TMGL). The thermoelastic coupling effect creates two types of coupled longitudinal waves which are dispersive as well as exhibit attenuation. Different from the thermoelastic coupling effect, there also exists one independent vertically shear‐type (SV‐type) wave. In contrast to the classical Green–Lindsay (GL) and Lord–Shulman (LS) theories of generalized thermoelasticity, the SV‐type wave is not only dispersive in nature but also experiences attenuation. Analytical expressions for the amplitude ratios and their respective energy ratios for reflected thermoelastic waves are determined when a coupled longitudinal wave is made incident on the free surface. The paper concludes with the numerical results on the phase speeds, amplitude ratios and their respective energy ratios for specific parameter choices. Various graphs have been plotted to analyze the behavior of these quantities. The characteristics of employing the 2TMGL model are discussed by comparing the numerical results obtained for the present model with those obtained in case of the two‐temperature Green–Lindsay (2TGL) and two‐temperature Lord–Shulman (2TLS) models.

show abstract

“…Many researchers (Abbas (2007), Abbas (2009), Abbas (2014aAbbas ( , 2014b, Abbas et al (2009), Alzahrani and Abbas (2016), , , Marin and Nicaise (2016), Mohamed et al (2009), Mondal (2019), Mondal (2020), Zenkour and Abbas (2014)) have solved several problems under generalized thermo-elastic theories. Moreover, other researchers (Bachher and Sarkar (2019), Bachher et al (2015), Biswas and Sarkar (2018), Ellahi et al (2019), , Marin and Craciun (2017, Mondal et al (2019), Sheikholeslami et al (2019), Zeeshan et al (2019)) have solved other problems for porous medium under different boundary conditions. In the Laplace's domain, the eigenvalues approach yielded an analytical solution without any supposed restrictions on the factual physical variables.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model

Hobiny

Abbas

2020

HFF

View full text Add to dashboard Cite

Purpose The purpose of this study is to use the generalized model for thermoelastic wave under the dual phase lag (DPL) model to compute the increment of temperature, the components of displacement, the changes in volume fraction field and the stress components in a two-dimensional (2D) porous medium. Design/methodology/approach Using Fourier and Laplace transformations with the eigenvalue technique, the exact solutions of all physical quantities are obtained. Findings The derived method is evaluated with numerical results, which are applied to the porous medium in a simplified geometry. Originality/value Finally, the outcomes are graphically represented to show the difference among the models of classical dynamical coupled, the Lord and Shulman and DPL.

show abstract

Fundamental solution of the steady oscillations equations in porous thermoelastic medium with dual-phase-lag model

Cited by 44 publications

References 20 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

Thermoelastic plane waves under the modified Green–Lindsay model with two‐temperature formulation

Generalized thermoelastic interaction in a two-dimensional porous medium under dual phase lag model

Contact Info

Product

Resources

About