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

Uniqueness of Solutions in Thermopiezoelectricity of Nonsimple Materials

This article presents the theory of thermopiezoelectricity in which the second displacement gradient and the second electric potential gradient are included in the set of independent constitutive variables. This is achieved by using the entropy production inequality proposed by Green and Laws. At first, appropriate thermodynamic restrictions and constitutive equations are obtained, using the well-established Coleman and Noll procedure. Then, the balance equations and the constitutive equations of linear theory are derived, and the mixed initial-boundary value problem is set. For this problem a uniqueness result is established. Next, the basic equations for the isotropic case are derived. Finally, a set of inequalities is obtained for the constant constitutive coefficients of the isotropic case that, on the basis on the previous theorem, ensure the uniqueness of the solution of the mixed initial-boundary value problem

Finite element modeling of effective properties of nanoporous thermoelastic composites with surface effects

This investigation concerns to the determination of the material properties of nanoscale thermoelastic composites of an arbitrary anisotropy class with stochastically distributed porosity. In order to take into account nanoscale level at the borders between material and pores, the GurtinMurdoch model of surface stresses and the highly conduct- ing model are used. Finite element package ANSYS was used to simulate representative volume and to calculate the effective material properties. This approach is based on the theory of effective moduli of composite mechanics, modeling of representative volumes and the finite element method. Here, the contact boundaries between material and pores were covered by the surface membrane elastic and thermal shell elements in order to take the surface effects into account

On the Extensional and Flexural of Generalized Thermoelastic Waves in an Anisotropic Plate

The propagation of extensional and flexural motions of generalized thermoelastic waves in a homogeneous, transversely isotropic plate of finite width is considered.  The frequency equations for the plates in closed form and suitable mathematical conditions for symmetric and antisymmetric wave modes propagation are derived. Numerical calculations for three various theories of generalized thermoelasticity is carried out. In each case the real and imaginary parts of the frequency equation as a function of phase velocity for different values of thermal relaxation times are illustrated graphically. It is found that, the frequency equations of the extensional and flexural motions can be oscillate with respect to the medial of the plate. Moreover, it gets modified due to the thermal relaxation times and anisotropic effects. Finally, the results for the coupled thermoelasticity can be obtained as particular cases of the results by setting thermal relaxation times equal to zero Keywords: Frequency equations; Extensional and flexural modes; Thermal relaxation times; Harmonic wave propagatio

Influence of rotation and initial stress on Propagation of Rayleigh waves in fiber-reinforced solidanisotropic magneto-thermo-viscoelastic media.

This paper is concerned with giving a mathematical model on the propagation of Rayleigh waves in a homogeneous magneto-thermo-viscoelastic,pre-stressed elastic half – space subjected to theinitial stress and rotation. The dispersion equation has been derived for a half-space, when both media are considered as pre-stressed and the effect of rotation and initial stressshown in earlier investigators.Numerical results have been obtained  in the physical domain. Numerical simulated results are depicted graphically to show the effect of rotation and magnetic field and initial stressonRayleigh wave velocity. Comparison was made with the results obtained in the presence and absence of the rotation , initial stressand magnetic field. The study shows that there is a variational effect of magneto-elasticityand rotation, initial stress on the Rayleigh wave velocity

Boundary Element Mathematical Modelling and Boundary Element Numerical Techniques for Optimization of Micropolar Thermoviscoelastic Problems in Solid Deformable Bodies

The main objective of this chapter is to introduce a new theory called three-temperature nonlinear generalized micropolar thermoviscoelasticity. Because of strong nonlinearity of simulation and optimization problems associated with this theory, the numerical solutions for problems related with the proposed theory are always very difficult and require the development of new numerical techniques. So, we propose a new boundary element technique for simulation and optimization of such problems based on genetic algorithm (GA), free form deformation (FFD) method and nonuniform rational B-spline curve (NURBS) as the shape optimization technique. In the formulation of the considered problem, the profiles of the considered objects are determined by FFD method, where the FFD control points positions are treated as genes, and then the chromosomes profiles are defined with the genes sequence. The population is founded by a number of individuals (chromosomes), where the objective functions of individuals are determined by the boundary element method (BEM). The numerical results verify the validity and accuracy of our proposed technique