Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium

The propagation of plane waves in fibre-reinforced media is discussed. The expressions of phase velocities of quasi-P (qP) and quasi-SV (qSV) waves propagating in plane symmetry are obtained in terms of propagation vectors. We have established a relation from which the displacement vector can be obtained in terms of the propagation vector. Expressions for the reflection coefficients of qP and qSV waves are obtained. Numerical results of reflection coefficients are obtained and presented graphically. The partition of energy between qP and qSV waves reflected on free and rigid boundaries due to incident qP and qSV waves are also obtained and presented graphically.     

Comments on “surface waves in fibre-reinforced anisotropic elastic media” by Sengupta and Nath [Sādhanā 26: 363–370 (2001)]

In the paper under discussion, the problem of surface waves in fibrereinforced anisotropic elastic media has been studied. The authors express the plane strain displacement components in terms of two scalar potentials to decouple the plane motion into P and SV waves. In the present note, we show that, for wave propagation in fibre-reinforced anisotropic media, this decoupling cannot be achieved by the introduction of the displacement potentials. In fact, the expressions for the displacement potentials used by the authors do not satisfy one of the equations of motion. Consequently, most of the equations and results of the subject paper are either irrelevant or incorrect     

Surface waves in fibre-reinforced anisotropic elastic media

The aim of this paper is to investigate surface waves in anisotropic fibre-reinforced solid elastic media. First, the theory of general surface waves has been derived and applied to study the particular cases of surface waves — Rayleigh, Love and Stoneley types. The wave velocity equations are found to be in agreement with the corresponding classical result when the anisotropic elastic parameters tends to zero. It is important to note that the Rayleigh type of wave velocity in the fibre-reinforced elastic medium increases to a considerable amount in comparison with the Rayleigh wave velocity in isotropic materials.     

平面S波在非饱和土自由边界上的反射问题研究

运用非饱和孔隙介质理论阐述了弹性波在非饱和土中的传播特性,分析了平面S波在非饱和土层自由边界上的反射问题。根据边界条件,分别导出了在非饱和土自由边界上的四种反射波：反射P1波、反射P2波、反射P3波及反射S波的振幅反射率及能量反射率的理论表达式,并在此基础上进行了数值计算。算例中讨论了四种反射波的振幅反射率及能量反射率受平面S波入射角度及土层饱和度变化的影响情况。计算结果表明：各反射波的振幅反射率及能量反射率不仅与入射角有关,也受到饱和度变化的影响,这些结论对土动力学的理论研究以及相关工程地震勘探具有一定指导意义。     

SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space

Summary A problem of reflection and transmission of a plane SH-wave incident at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space is investigated. Rayleigh's method of approximation is applied to derive the reflection and transmission coefficients for the first and second order approximation of the corrugation. The expressions for reflection and transmission coefficients for the first order approximation of the corrugation are obtained in closed form for a special type of interface, and the energy partition relation is derived. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of elastic properties of the half-spaces and also of the angle of incidence. Numerical examples illustrating the effects of the sandiness, the anisotropy, the corrugation of the interface, the frequency, and the angle of the incidence on the coefficients are presented.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Reflection of PlaneWaves from Electro-magneto-thermoelastic Half-space with a Dual-Phase-Lag Model

The aim of this paper is to study the reflection of plane harmonic waves from a semi-infinite elastic solid under the effect of magnetic field in a vacuum. The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves, are obtained. Similarly, the reflection coefficient ratio variations with the angle of incident under different conditions are shown graphically. Comparisons are made with the results predicted by the dual-phase-lag model and Lord-Shulman theory in the presence and absence of magnetic field.     

A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation

The theory of thermoelasticity with energy dissipation is employed to study plane waves in a fibre-reinforced anisotropic thermoelastic half-space. We apply a thermal shock on the surface of the half-space which is taken to be traction free. The problem is solved numerically using a finite element method. Moreover, the numerical solutions of the non-dimensional governing partial differential equations of the problem are shown graphically. Comparisons are made with the results predicted by Green–Naghdi theory of the two types (GNII without energy dissipation) and (GNIII with energy dissipation). We found that the reinforcement has great effect on the distribution of field quantities. Results carried out in this paper can be used to design various fibre-reinforced anisotropic thermoelastic elements under thermal load to meet special engineering requirements.     

Reflection of plane waves at the initially stressed surface of a fiber-reinforced thermoelastic half space with temperature dependent properties

In this paper, a model of two dimensional problem of generalized thermoelasticity for a fiber-reinforced anisotropic elastic medium under the effect of temperature dependent properties is established. Reflection phenomena of plane waves in an initially stressed thermoelastic medium is studied in the context of two theories proposed by Lord–Shulman and Green–Lindsay. Using proper boundary conditions, the amplitude ratios and energy ratios for various reflected waves are presented. The phase speeds, reflection coefficients and energy ratios are computed numerically with the help of MATLAB programming and are depicted graphically to show the effect of initial stress and temperature dependent properties. It is found that there is no dissipation of energy at the boundary surface during reflection. A comparison between the two theories is also depicted in the present investigation.

     

Interface waves along an anisotropic imperfect interface between anisotropic solids

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.     

The effect of rotation on the reflection of magneto-thermoelastic waves under thermoelasticity without energy dissipation

Summary In this paper reflection of magneto-thermoelastic waves is employed to study the effect of rotation and the magnetic field on the plane harmonic waves of a rotating semi-infinite elastic solid nearby a vacuum under Green and Naghdi theory. The expressions for the reflection coefficients, which are the ratios of the amplitudes of the reflected waves to the amplitude of the incident wave, are obtained. The effect of rotation, the magnetic field, coupling parameter and frequency on the reflection ratios are illustrated graphically. Comparisons are made with the results predicted by GN theory of type II in the presence and absence of rotation and magnetic field. A comparison is also made with the results predicted by GN theory of types II and III in the presence of the magnetic field and rotation.     

Reflection of Magneto-Thermoviscoelastic Waves Under Generalized Thermoviscoelasticity

Considering each of the thermal fields, viscoelastic and electromagnetic fields contribute to the total deformation of a body and interact with each other. Reflection of magneto-thermoelastic waves under generalized thermoviscoelastic theories is employed to study the reflection of plane harmonic waves from a semi-infinite elastic solid in a vacuum. The expressions for the reflection coefficients, which are the ratios of the amplitudes of the reflected waves to the amplitudes of the incident waves, are obtained, and the reflection coefficient ratios variation with the angle of incidence under different conditions are shown graphically when acrylic plastic materials are considered.     

Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media

The propagation of inhomogeneous and elliptically polarized plane waves in absorbing uniaxial anisotropic media is described using complex unitary vectors to represent the direction of propagation and the direction of polarization. Detailed expressions for electric displacement, electric field, and magnetic field vectors are obtained for the ordinary and extraordinary waves, and their geometry is discussed. According to the complex direction of propagation, three particular cases are studied: the real case (homogeneous wave), the case perpendicular to the optical axis, and the case coplanar with the optic axis. The case of isotropic media is also analyzed.     

Effect of the interrelationship of thermal and mechanical fields on the propagation of wave motions in cubically anisotropic thermoelastic materials

A characteristic equation for a system of equations of motion of a cubically anisotropic medium with allowance for the relaxation time of thermal disturbances has been obtained, and expressions for the velocities of propagation of modified elastic and thermal waves have been found. The surfaces of inverse velocities have been constructed and the influence of the effect of interrelationship of thermal and mechanical fields on the change in the phase velocities of propagation of a quasilongitudinal elastic wave and a thermal wave in different planes of a cubically anisotropic material has been analyzed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 384–388, March–April, 2008.     

A note on energy flux in micropolar elastic waves

The expressions for the time average power per unit area, the kinetic energy per unit volume, strain energy per unit volume and velocity of energy flux are derived for the case of a plane time harmonic micropolar elastic waves and it has been shown that the time-average energy density is equally divided between the time-averages of the kinetic and strain energy densities. The energy ratios of reflected micropolar elastic waves with the angle of emergence of incident longitudinal displacement wave have been shown graphically.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Viscously damped acoustic waves with the lattice Boltzmann method

Acoustic wave propagation in lattice Boltzmann Bhatnagar-Gross-Krook simulations may be analysed using a linearization method. This method has been used in the past to study the propagation of waves that are viscously damped in time, and is here extended to also study waves that are viscously damped in space. Its validity is verified against simulations, and the results are compared with theoretical expressions. It is found in the infinite resolution limit k→0 that the absorption coefficients and phase differences between density and velocity waves match theoretical expressions for small values of ωτ(ν), the characteristic number for viscous acoustic damping. However, the phase velocities and amplitude ratios between the waves increase incorrectly with (ωτ(ν))(2), and agree with theory only in the inviscid limit k→0, ωτ(ν)→0. The actual behaviour of simulated plane waves in the infinite resolution limit is quantified.     

Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags

The present paper deals with the investigation of the propagation of harmonic plane waves with assigned frequency by employing the thermoelasticity theory with dual-phase-lags (Tzou [7], Chandrasekharaiah [10]). The exact dispersion relation solutions for the plane wave are obtained analytically and asymptotic expressions of several characterizations of the wave fields, such as phase velocity, specific loss, penetration depth and amplitude ratios are obtained for both the high frequency as well as low frequency values. In order to illustrate the analytical results, the computational tool Mathematica is used to find the numerical values of different wave fields at intermediate values of frequency and results are depicted in different figures. A detailed analysis of the effects of phase-lags on plane wave is presented on the basis of analytical and numerical results and significant points are highlighted.     

Existence of longitudinal waves in anisotropic poroelastic solids

In anisotropic fluid-saturated porous solids, four waves can propagate along a general phase direction. However, solid particles in different waves may not vibrate in mutually orthogonal directions. In the propagation of each of these waves, the displacement of pore–fluid particles may not be parallel to that of solid particles. The polarization for a wave is the direction of aggregate displacement of the particles of the two constituents of a porous aggregate. These polarizations, for different waves, are not mutually orthogonal. Out of the four waves in anisotropic poroelastic medium, two are termed as quasi-longitudinal waves. The prefix ‘quasi’ refers to their polarization being nearly, but not exactly, parallel to the direction of propagation. The existence of purely longitudinal waves in an anisotropic poroelastic medium is ensured by the stationary characters of two expressions. These expressions involve the elastic (stiffness and coupling) coefficients of a porous aggregate and the components of phase direction. Necessary and sufficient conditions for the existence of longitudinal waves are discussed for different anisotropic symmetries. Conditions are also discussed for the existence of the apparent longitudinal waves, i.e., the propagation of wave motion with the particle displacement parallel to the ray direction instead of the phase direction. A graphical solution of a numerical example is shown to check the existence of these apparent longitudinal waves for general directions of phase propagation.     

A fully dynamic theory of piezoelectromagnetic waves

The Maxwell’s equations, coupled to the mechanical equations of motion, are studied here based on the standard spaces of the physical presentation. The complete set of uncoupled and fully dynamic equations of waves in anisotropic piezomagnetic media is deduced, in which the equations of electromagnetic waves and elastic ones are both of order 4. The results show that the number of electromagnetic and elastic waves is determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behavior of piezoelectromagnetic waves in the piezomagnetic material of class 6mm; the electromagnetic waves with the speed of elastic waves and elastic waves with the speed of electromagnetic waves are obtained.