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

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

A mathematical model of shear wave propagation in the incompressible transversely isotropic thermoelastic half-spaces

This article deals with the problem of reflection and transmission of shear waves at a plane interface between two dissimilar incompressible transversely isotropic thermoelastic half-spaces. Two coupled quasi-shear waves are found to propagate due to the incompressibility of such materials. Applying appropriate boundary conditions at the plane interface, amplitude ratios of the reflected and transmitted quasi-shear waves are obtained. It has been observed that these ratios are functions of the angle of incidence, elastic and thermal parameters of the materials. These ratios are computed numerically for a particular model to see the effects of specific heat and thermal expansion on quasi-shear waves in incompressible transversely isotropic thermoelastic materials. The results are also presented graphically

Reference Temperature Dependent Thermoelastic Solid with Voids Subjected to Continuous Heat Sources

In the present article, the reference temperature dependency Lord--Shulman model of generalized thermoelasticity with voids subjected to a continuous heat source in a half-space is discussed. The Laplace transform together with eigenvalue approach technique is applied to find a closed-form solution for the physical variables viz. distribution of temperature, volume fraction field, deformation and stress field in the Laplace transform domain. The numerical inversions of those physical variables in the space-time domain are carried out by using the Zakian algorithm for the inversion of the Laplace transform. Numerical results are shown graphically and the results obtained are analyzed

Viscothermoelastic waves in a gravitated piezoelectric multilayered LEMV /CFRP cylinder coated with thin film

The present paper is concerned the effects of gravitational force and rotation in a composite multilayered hollowcylinder which contain inner and outer piezo-thermoelasticity layers bonded by Linear Elastic Material with Voids (LEMV) withinthe frame of dual-phase-lag model.Also the composite multilayered hollow cylinder coated with thin film is considered.Theequation of displacement components, temperature, and electric are obtained using linear theory of elasticity. The dispersionequations are acquired by means of traction free boundary conditions and are numerically analyzed for CdSe material.Theenumerated frequency, thermal and electrical nature against wave number in the presence of gravatity and rotation is presentedgraphically. Adhesive layer LEMV is compared with Carbon Fiber Reinforced Polymer (CFRP) in presence of gravity androtation

Mathematical modelling of Stoneley wave in a transversely isotropic thermoelastic media

This paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar transversely isotropic thermoelastic solids without energy dissipation and with two temperatures. The secular equation of Stoneley waves is derived in the form of the determinant by using appropriate boundary conditions i.e. the stresses components, the displacement components, and temperature at the boundary surface between the two media are considered to be continuous at all times and positions . The dispersion curves giving the Stoneley wave velocity and Attenuation coefficients with wave number are computed numerically. Numerical simulated results are depicted graphically to show the effect of two temperature and anisotropy on resulting quantities. Copper material has been chosen for the medium and magnesium for the medium Some special cases are also deduced from the present investigation

Fractional order magneto-thermoelasticity in a rotating media with one relaxation time

The theory of generalized thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative is used to study magneto-thermoelastic response of a homogeneous isotropic two-dimensional rotating elastic half-space solid. The solution for the physical variables is obtained using the normal mode analysis together with an eigenvalue approach technique. Numerical computations are carried out for a hypothetical copper like material the numerical results are illustrated graphically. Some comparisons have been made in the graphical results to show the effect of fractional parameter, magnetic field and the rotation on the field variables

(R1056) Effect of Rotation on Plane Waves of Generalized Magneto-thermoelastic Medium with Voids under Thermal Loading due to Laser Pulse

The investigation in this paper deals with the rotation of the magneto-thermoelastic solid and with voids subjected to thermal loading due to laser pulse. The problem is studied in the context of three theories of generalized magneto thermoelasticity: Lord-Schulman (L-S), Green-Lindsay (G-L) and the coupled theory (CD) with the effect of rotation, magnetic field, thermal loading and voids. The methodology applied here is using the normal mode analysis to solve the physical problem to obtain the exact expressions for the displacement components, the stresses, the temperature, and the change in the volume fraction field have been shown graphically by comparison between three theories, in the presence and the absence of rotation, magnetic field and for two different values of time on thermoelastic material in the presence of voids

Pulsed Laser Heating of a Thermoelastic Medium with Two-temperature under Three-phase-lag Model

In this paper, the problem of the generalized thermoelastic medium for three different theories under the effect of a laser pulse and two-temperature is investigated. The Lord–Shulman (L-S), Green-Naghdi of type III (G-N III) and three-phase-lag (3PHL) theories are discussed with two-temperature. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, thermodynamic temperature and conductive temperature. The numerical results are given and presented graphically and the thermal force was applied. Comparisons are made with the results predicted by (3PHL), (G-N III) and (L-S) in the presence and absence of two-temperature. The boundary plane surface is heated by a non-Gaussian laser beam

A unifying perspective: the relaxed linear micromorphic continuum

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict non-polar size-effects. It is intended for the homogenized description of highly heterogeneous, but non polar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models