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1
Content available Generalized plane waves in a rotating thermoelastic double porous solid
Pathania Vijayata, Kumar Rajesh, Gupta Vipin, Barak M. S.
International Journal of Applied Mechanics and Engineering
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2022
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Vol. 27, no. 4
138--154
EN
The propagation of plane waves in a rotating homogeneous, isotropic, thermoelastic solid with double porosity following Lord-Shulman’s theory of thermoelasticity has been investigated. It is assumed that the medium rotates about an axis normal to the surface with a uniform angular velocity. There may exist five coupled waves that evolved due to the longitudinal, transverse disturbance, voids of type-I and type-II, and temperature change in the medium. The secular equation for the model under consideration has been derived with the help of formal solutions and boundary conditions. The amplitude of displacements, temperature change and volume fraction fields for voids of type-I and type-II have also been computed analytically. Finally, numerical computations have been carried out for magnesium crystal material to understand the behavior of amplitude of phase velocity, penetration depth, specific loss, displacement components, temperature change, and volume fraction field due to type-I and type-II voids corresponding to the different rotation rates. Various graphs have been plotted to support the analytical findings. The study may be used in the development of rotation sensors, material design and thermal efficiency.
2
Content available remote Reflection of plane waves from surface of a generalized thermo-viscoelastic porous solid half-space with impedance boundary conditions
Singh B.
Mechanics and Mechanical Engineering
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2018
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Vol. 22, nr 4
1483--1496
EN
A phenomenon of reflction of plane waves from a thermally insulated surface of a solid half-space is studied in context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions at free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of impedance parameter and the angle of incidence.
3
Content available remote Reflection of Plane Waves from Surface of a Generalized Thermo-viscoelastic Porous Solid Half-space with Impedance Boundary Conditions
Singh B.
Computational Methods in Science and Technology
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2018
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Vol. 24, No. 4
273--283
EN
A phenomenon of reflection of plane waves from a thermally insulated surface of a solid half-space is studied in the context of Lord-Shulman theory of generalized thermo-viscoelasticity with voids. The governing equations of generalized thermo-viscoelastic medium with voids are specialized in x-z plane. The plane wave solution of these equations shows the existence of three coupled longitudinal waves and a shear vertical wave in a generalized thermo-viscoelastic medium with voids. For incident plane wave (longitudinal or shear), three coupled longitudinal waves and a shear vertical wave reflect back in the medium. The mechanical boundary conditions on the free surface of solid half-space are considered as impedance boundary conditions, in which the shear force tractions are assumed to vary linearly with the tangential displacement components multiplied by the frequency. The impedance corresponds to the constant of proportionality. The appropriate potentials of incident and reflected waves in the half-space will satisfy the required impedance boundary conditions. A non-homogeneous system of four equations in the amplitude ratios of reflected waves is obtained. These amplitude ratios are functions of material parameters, impedance parameter, angle of incidence, thermal relaxation and speeds of plane waves. Using relevant material parameters for medium, the amplitude ratios are computed numerically and plotted against certain ranges of the impedance parameter and the angle of incidence.
4
Content available Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids
Bijarnia R., Singh B.
International Journal of Applied Mechanics and Engineering
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2016
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Vol. 21, no. 2
285--301
EN
The paper is concerned with the propagation of plane waves in a transversely isotropic two temperature generalized thermoelastic solid half-space with voids and rotation. The governing equations are modified in the context of Lord and Shulman theory of generalized thermoelasticity and solved to show the existence of four plane waves in the x – z plane. Reflection of these plane waves from thermally insulated stress free surface is also studied to obtain a system of four non-homogeneous equations. For numerical computations of speed and reflection coefficients, a particular material is modelled as transversely isotropic generalized thermoelastic solid half-space. The speeds of plane waves are computed against the angle of propagation to observe the effects of two temperature and rotation. Reflection coefficients of various reflected waves are also computed against the angle of incidence to observe the effects of various parameters.
5
Content available Reflection of plane waves from a free surface of a generalized magneto-thermoelastic solid half-space with diffusion
Singh B., Singh L., Deswal S.
Journal of Theoretical and Applied Mechanics
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2014
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Vol. 52 nr 2
385--394
EN
Green-Naghdi’s theory of generalized thermoelasticity is applied to study the reflection of P and SV waves from the free surface of a magneto-thermoelastic solid half-space. The boundary conditions are satisfied by appropriate potential functions to obtain a system of four non-homogeneous equations in reflection coefficients. The reflection coefficients depend upon the angle of incidence of P and SV waves, magnetic field, thermal field, diffusion parameters and other material constants. The numerical values of the modulus of the reflection coefficients are shown graphically with the angle of incidence of P and SV waves. The effect of magnetic field is observed significantly on various reflected waves.
6
Content available remote Reflection of transverse and microrotational waves from free surface in micropolar thermodiffusion elastic half-space
Kumar R., Kaushal S., Sharma K. D., Garg S. K.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 2
401-417
EN
The problem of reflection of plane waves in a micropolar thermodiffusion elastic is investigated in the context of the coupled theory. The amplitude ratios of various reflected waves are continuous functions of the angle of incidence and material parameters of the medium. A graphical representation of amplitude ratios is presented and the impact of micropolarity and diffusion property of the medium is observed to be significant. Some special cases of interest are deduced from the present article.
7
Content available remote Reflection of transverse and microrotational waves from free surface in micropolar thermodiffusive elastic half-space
Kumar R., Kaushal S., Sharma K. D., Garg S. K.
International Journal of Applied Mechanics and Engineering
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2012
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Vol. 17, no. 1
143-159
EN
The problem of reflection of plane waves in a micropolar thermodiffusive elastic has been investigated in the context of coupled theory. The amplitude ratios of various reflected waves are continuous function of the angle of incidence and material parameters of the medium. A graphical representation of amplitude ratios is presented and the impact of micropolarity and diffusive property of the medium is observed to be significant. Some special cases of interest are deduced.
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