Reflection of plane waves at the free surface of a monoclinic thermoelastic solid half-space

Lord–Shulman and Green–Lindsay theories of generalized thermoelasticity are applied to study the reflection from a thermally insulated stress-free thermoelastic solid half-space of monoclinic type. A particular model is chosen for the numerical computations of reflection coefficients. Effects of anisotropy and relaxation times are observed on reflection coefficients.     

Propagation of plane waves in an anisotropic thermoelastic half-space

International Applied Mechanics -     

Analysis of plane waves in anisotropic thermoelastic diffusive medium

This paper concentrates on the study of the propagation of harmonic plane waves in a homogeneous anisotropic thermoelastic diffusive medium in the context of different theories of thermoelastic diffusion. It is found that five types of waves propagate in an anisotropic thermoelastic diffusive medium, namely a quasi-elastodiffusive (QED-mode), two quasi-transverse (QSH-mode and QSV-mode), a quasi-mass diffusive (QMD-mode) and a quasi-thermo diffusive (QTD-mode) wave. The governing equations for homogeneous transversely isotropic diffusive medium in different theories of thermoelastic diffusion are taken as a special case. It is noticed that when plane waves propagate in one of the planes of transversely isotropic thermoelastic diffusive solid, purely quasitransverse wave mode(QSH) decouples from rest of the motion and is not affected by the thermal and diffusion vibrations. On the other hand, when plane waves propagate along the axis of solid, two quasi-transverse wave modes (QSH and QSV) decouple from the rest of the motion and are not affected by the thermal and diffusion vibrations. From the obtained results, the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically for a single crystal of magnesium. The effects of diffusion and relaxation times on phase velocity, attenuation coefficient, specific loss and penetration depth has been studied. Some particular cases are also discussed.     

On the propagation of thermoelastic waves in temperature rate-dependent materials

The one-dimensional propagation of thermoelastic waves in isotropic homogeneous half spaces within the theory of Green and Lindsay [1] is studied. Padé-extended ray methods are employed to obtain the desired information. Comparisons between the predictions of the Green and Lindsay theory and the theory of Lord and Shulman [2] are made. Our ray series solutions show that for discontinuous thermal disturbances the displacement according to the Green and Lindsay theory is also discontinuous. This violates the fundamental continuum hypothesis that matter is impenetrable. For a simple numerical example we show also that a compressive behaviour in the displacement may be associated with a tensile behaviour in the stress and vice versa. This prediction of the Green and Lindsay theory is also unrealistic from the physical point of view.     

Reflection of plane waves under initial stresses at a free surface

The paper deals with the phenomenon of reflection of plane elastic waves in a free surface when the medium is initially stressed. It has been shown analytically that the reflected P and SV waves depend on initial stresses present in the medium. The numerical values of reflection coefficients for different initial stresses and the angle of incidence have been calculated by the Computer I.C.L. 1901-A and the results are given in the form of graphs. Many interesting results are found in the paper which are not seen in an initially stress-free medium.     

Reflection and refraction of plane waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures

The problem of reflection and refraction of waves at the interface of an elastic solid and microstretch thermoelastic solid with microtemperatures has been investigated. It is shown that due to incidence of P-wave or SV-wave at the interface, the waves are reflected and refracted. The amplitude ratios of these various reflected and refracted waves have been computed numerically, and graphical representation of their variations is made with the angle of incidence. Effect of microrotation on these amplitude ratios has been shown graphically. Some particular cases of interest have also been discussed.     

Reflection and transmission of plane waves at the interface of an elastic half-space and a fractional order thermoelastic half-space

The problem of reflection and transmission due to longitudinal and transverse waves incident obliquely at a plane interface between uniform elastic solid half-space and fractional order thermoelastic solid half-space has been studied. It is found that the amplitude ratios of various reflected and refracted waves are functions of angle of incidence and frequency of incident wave and are influenced by the fractional order thermoelastic properties of media. The expressions of amplitude ratios and energy ratios have been computed numerically for a particular model. The variation of amplitude and energy ratios with angle of incidence is shown graphically. The conservation of energy at the interface is verified.     

Rayleigh surface waves in the theory of thermoelastic materials with voids

In this paper we analyze the behavior of plane harmonic waves and Rayleigh waves in a linear thermoelastic material with voids. We take into account the damped effects of the thermal field upon the propagation waves. Consequently, the propagation condition is established in the form of an algebraic equation of 9th degree whose coefficients are complex numbers while the eigensolutions of the thermoelastodynamic with voids system are explicitly obtained in terms of the characteristic solutions. We show that the transverse waves are undamped in time and they are not influenced by the thermal and porous effects while the longitudinal waves are all damped in time and they are coupled with the thermal and porous effects. The related solution of the Rayleigh surface wave problem is expressed as a linear combination of the eigensolutions in concern. The secular equation is established in an implicit form and afterwards an explicit form is written for an isotropic and homogeneous thermoelastic with voids half-space. Furthermore, we use the numerical methods and computations to solve the secular equation for a specific material.     

Reflection and refraction of plane waves under initial stresses at an interface

The paper deals with the phenomena of reflection and refraction of plane elastic waves at a plane interface between two semi-infinite elastic solid media in contact, when both the media are initially stressed. It has been shown analytically that both reflected and refracted P and SV waves depend on initial stresses present in the media. The numerical values of reflection and refraction coefficients for different initial stresses and the angle of incidence have been calculated by computer and the results are given in the form of graphs. Many results are found in the paper which are not seen in initially stress-free media.     

The propagation and growth of acceleration waves in constrained thermoelastic materials

Propagation conditions are derived for a thermoelastic material subject to arbitrary thermo-kinematic constraints. The results are rendered more concise by rephrasing existing thermodynamic theories for constrained materials in such a way, that the constraint equations may be absorbed into the free energy function. Propagation conditions for homothermal and homentropic waves are shown to be of Fresnel-Hadamard type. Equations governing the growth of acceleration amplitude are also derived for plane homothermal or homentropic waves; these are shown to be similar to the corresponding equations for unconstrained materials.     

Propagation of plane waves in thermoelastic cubic crystal material with two relaxation times

A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated. The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem. The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance, slip and welded boundaries. Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence have been compared graphically for different incident waves. It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media.     

Reflection for three-dimensional plane waves in triclinic crystalline medium

The propagation of three-dimensional plane waves at a traction free boundary of a half-space composed of triclinic crystalline material is discussed.A method has been developed to find the analytical expressions of all the three phase velocities of quasi-P (qP),quasi-SV(qSV)and quasi-SH(qSH)in three dimensions.Closed form expressions in three dimensions for the amplitude ratios of reflection coefficients of qP,qSV and qSH waves in a triclinic medium are obtained.These expressions are used for numerically studying the variation of the reflection coefficients with the angle of incidence.The graphs are drawn for different polar angle and azimuth.Numerical results presented indicate that the anisotropy affect the reflection coefficients significantly in the three dimensional case compared to the two-dimensional case.     

Dispersive waves in microstructured solids

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler–Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.     

On the types and number of plane waves in hypoelastic materials

General principles are formulated for modeling the elastic deformation of materials and analyzing plane waves in nonlinearly elastic materials such as hyperelastic, hypoelastic, and those governed by the general law of elasticity. The results of studying the propagation of plane waves in hypoelastic materials are further outlined. The influence of initial stresses and initial velocities on the types and number of plane waves is studied. Wave effects characteristic of hypoelastic materials are predicted theoretically. One of such effects is blocking of certain types of plane waves by initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 11, pp. 96–107, November 2005.     

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

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.     

The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media

The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints are investigated for classes of constraints broad enough to encompass all those encountered in practice. Attention is focussed on principal waves, and results are presented for the growth of the amplitudes of such waves first for fronts of arbitrary curvature, and subsequently by specialisation for plane, cylindrical and spherical waves travelling in material which has undergone one-dimensional plane deformation, cylindrically symmetric and spherically symmetric deformation, respectively.     

Reflection and transmission of plane waves from fluid-piezothermoelastic solid interface

The reflection and transmission of plane waves from a fluid-piezothermoelastic solid interface are studied. The expressions for amplitude ratios and energy ratios corresponding to reflected waves and transmitted waves are derived analytically. The piezo-thermoelastic solid half-space is assumed to have 6mm type symmetry and assumed to be loaded with water. The effects of angle of the incidence, the frequency, the specific heat, the relaxation time, and the thermal conductivity on the reflected and transmitted energy ratios are studied numerically for a particular model of cadmium selenide (CdSe) and water. Some special cases are also studied.     

Reflection and transmission of plane waves by layered periodic media

The reflection and transmission coefficients (at normal incidence) for plane parallel slabs consisting of N inhomogeneous and exactly identical parallel layers are expressed in terms of the corresponding coefficients for a single layer. The analysis is effected by two different methods, one of which stems from the so called invariant imbedding viewpoint while the other relies on a more conventional matrix argument.