The present investigation is concerned with wave propagation in micropolar thermoelastic solid half space with distinct conductive and thermodynamic temperatures. Reflection of plane waves incident obliquely at the free surface of micropolar generalized thermoelastic solid half space with two temperature is investigated. Amplitude ratios various reflected waves are obtained in closed form and it is found that these are function of angle of incidence, frequency and are affected by the micropolar thermoelastic properties of the medium. Effect of two temperatures is shown on these amplitude ratios for a specific model. Results of some earlier workers have also been deduced from the present investigation as a special case.

http://www.scientificbulletin.upb.ro/rev_docs_arhiva/rezee8_437046.pdf

Effect Of Distinct Conductive And Thermodynamic Temperatures On The Reflection Of Plane Waves In Micropolar Elastic Half-Space

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.

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Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

The propagation of plane vertical transverse waves at an interface of a semi-infinite piezoelectric elastic medium under the influence of the initial stresses is discussed. The free surface of the piezoelectric elastic medium is considered to be adjacent to vacuum. We assumed that the piezoelectric material is anisotropic of the type of a transversely isotropic crystals (hexagonal crystal structure, class 6 mm). For an incident of vertical transverse plane wave, four types (two for the displacement and two for the electric potential) of reflected plane waves, called quasi-longitudinal (qP) and quasi-shear vertical (qSV) waves are shown to be exist. The relations governing the reflection coefficients of these reflected waves for various boundary conditions (mixed-free-fixed) are derived. It has been shown analytically that reflected coefficients of (qP) and (qSV) waves depend upon the angle of incidence, the parameters of electric potential, the material constants of the medium as well as the initial stresses presented in the medium. The numerical computations of reflection coefficients for different values of initial stresses have been carried out by computer for aluminum nitride (AlN) as an example and the results are given in the form of graphs. Finally, particular cases are considered in the absence of the initial stresses and the electric potential. Some of earlier studies have been compared to the special cases and shown good agreement with them.

The reflection phenomena of quasi-vertical transverse waves in piezoelectric medium under initial stresses

Thermomechanical interactions in transversely isotropic magnetothermoelastic medium with vacuum and with and without energy dissipation with combined effects of rotation, vacuum and two temperatures

The present investigation is concerned with two problems. (i) Reection and transmission of thermoelastic waves between two thermoelastic half-spaces with two temperature at an imperfect interface; and (ii) Propagation of Rayleigh waves at the free surface of thermoelastic solid with two temperature. In problem (i) the amplitude ratios for reection and transmission coecients are obtained and deduced for normal force stiness, transverse force stiness, thermal contact conductance and perfect bonding. The numerical results obtained have been illustrated graphically to understand the behavior of amplitude ratios versus angle of incidence of longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. It is found that the amplitude ratios of various reected and transmitted waves are aected

Wave propagation in temperature rate dependent thermoelasticity with two temperatures

In this work, a two dimensional problem in electromagnetic micropolar generalized thermoelastic medium, in the presence of a transverse magnetic field subjected to mechanical force or thermal source (concentrated or uniformly distributed), is investigated. The entire elastic medium is rotating with a uniform angular velocity. Laplace and Fourier transform techniques are used to solve the problem and the Descartes’ method along with irreducible case of Cardan’s method is used to obtain the roots of eight degree equation. The transformed components of normal strain, normal stress, tangential couple stress, temperature distribution, induced electric field and magnetic field are obtained. The integral transforms have been inverted by using a numerical technique. Magnetic effects and effect of rotation have been depicted graphically on the resulting quantities. Particular cases of interest are also deduced from the present investigation.

Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources

The problem of reflection and transmission of plane waves incident on the contact surface of an elastic solid and an electro-microstretch generalized thermoelastic solid is discussed. It is found that there exist five reflected waves, i.e., longitudinal displacement (LD) wave, thermal (T) wave, longitudinal microstretch (LM) wave and two coupled transverse displacement and microrotational (CD(I) and CD(II)) waves in the electro-microstretch generalized thermoelastic solid, and two transmitted waves, i.e., longitudinal (P) and transverse (SV) waves in the elastic solid. The amplitude ratios of different reflected and transmitted waves are obtained for an imperfect boundary and deduced for normal force stiffness, transverse force stiffness, and perfect bonding. The variations of amplitude ratios with incidence angles have been depicted graphically for the LD wave and the CD(I) wave. It is noticed that the amplitude ratios of reflected and transmitted waves are affected by the stiffness, electric field, stretch, and thermal properties of the media. Some particular interest cases have been deduced from the present investigations.

Propagation of plane waves at the imperfect boundary of elastic and electro-microstretch generalized thermoelastic solids

The present investigation is concerned with wave propagation in an electro-microstretch generalized thermoelastic solid half space. Two different cases have been discussed: (i) reflection of plane wave at the free surface of an electro-microstretch generalized thermoelastic solid; and (ii) propagation of Rayleigh waves in an electro-microstretch generalized thermoelastic solid half space. In case (i), the amplitude ratios of the various reflected waves have been computed numerically and depicted graphically against angle of incidence. In case (ii), the frequency equation is derived and dispersion curves giving phase velocity and attenuation coefficient as a function of wave number, have been plotted graphically for a specific model. Some special cases of interest are also deduced, for both the cases.

Propagation of waves in an electro-microstretch generalized thermoelastic semi-space

The present investigation is concerned with a two-dimensional problem in electromagnetic micropolar elasticity for a half-space whose surface is subjected to distributed (concentrated or continuous) thermo-mechanical sources in the presence of a transverse magnetic field. As an application of the approach, the sources are taken as uniformly or linearly distributed. Laplace and Fourier transform techniques are used to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, normal stress, tangential couple stress, and temperature distribution in the physical domain. Magnetic effects on the components of normal strain, normal stress, tangential couple stress, and temperature distribution have been depicted graphically for two different theories of generalized thermoelasticity, Lord and Shulman (L–S) theory and Green and Lindsay (G–L) theory. A particular case of interest is also deduced from the present investigation.

Thermo-mechanical Deformation in Magneto-micropolar Elastic Medium

The present investigation is concerned with an axi-symmetric problem in the electromagnetic micropolar thermoelastic half-space whose surface is subjected to the mechanical or thermal source. Laplace and Hankel transform techniques are used to solve the problem. Various types of sources are taken to illustrate the utility of the approach. Integral transforms are inverted by using a numerical technique to obtain the components of stresses, temperature distribution, and induced electric and magnetic fields. The expressions of these quantities are illustrated graphically to depict the magnetic effect for two different generalized thermoelasticity theories, i.e., Lord and Shulman (L-S theory) and Green and Lindsay (G-L theory). Some particular interesting cases are also deduced from the present investigation.

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Papers

Effect of rotation in magneto-micropolar thermoelastic medium due to mechanical and thermal sources

Propagation of plane waves at the imperfect boundary of elastic and electro-microstretch generalized thermoelastic solids

Propagation of waves in an electro-microstretch generalized thermoelastic semi-space

Thermo-mechanical Deformation in Magneto-micropolar Elastic Medium

Elastodynamics of axi-symmetric deformation in magneto-micropolar generalized thermoelastic medium