Propagation Of Plane Harmonic Waves Research Articles

Wave propagation through an interface between viscoelastic media in the presence of defects

The propagation of plane harmonic waves through an interface between viscoelastic media is considered using the equations of field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. The reflection and refraction coefficients of elastic displacement waves and the waves of a defect field characterized by a dislocation density tensor and a defect flux tensor are determined. Dependences of the obtained quantities on the parameters of the interfacing media are analyzed.

Wave propagation characterization and design of two-dimensional elastic chiral metacomposite

In this work, a chiral metacomposite is proposed by integrating two-dimensional periodic chiral lattice with elastic metamaterial inclusions for low-frequency wave applications. The plane harmonic wave propagation in the proposed metacomposite is investigated through the finite element technique and Bloch's theorem. Band diagrams are obtained to illustrate wave properties of the chiral metacomposite. Effective dynamic properties of the chiral metacomposite are numerically calculated to explain low-frequency bandgap behavior in the chiral metacomposite. Interestingly doubly negative effective density and modulus of the chiral metacomposite are found in a specific frequency range, where a pass band with negative group velocity is observed. Tuning of the resulting low-frequency bandgaps is then discussed by adjusting microstructure parameters of the metamaterial inclusion and lattice geometry. Specifically design of a metacomposite beam structure for the broadband low-frequency vibration suppression is demonstrated.

The Generalized Relativistic Kinetic and Hydrodynamic Theory—Part I

On the basis of statistical description the motion of relativistic particles without external forces is considered. The generalized relativistic non-local Euler hydrodynamic equations are derived and investigated, including the limiting cases of the theory. The theory is applied to the propagation of plane harmonic waves of small amplitudes through a relativistic gas at rest. These results lead to construction of the relativistic quantum hydrodynamics.

Reflection of attenuated waves at the surface of a porous solid saturated with two immiscible viscous fluids

SUMMARY The mathematical model for wave motion in a porous solid saturated by two immiscible fluids is solved for the propagation of harmonic plane waves along a general direction in 3-D space. The solution is obtained in the form of Christoffel equations, which are solved further to calculate the complex velocities and polarisations of three longitudinal waves and one transverse wave. For any of these four attenuated waves, a general inhomogeneous propagation is considered through a particular specification of complex slowness vector. Inhomogeneity of an attenuated wave is represented through a finite non-dimensional parameter. For an arbitrarily chosen value of this inhomogeneity parameter, phase velocity and attenuation of a wave are calculated from the specification of its slowness vector. This specification enables to separate the contribution from homogeneous propagation of attenuated wave to the total attenuation. The phenomenon of reflection is studied to calculate the partition of wave-induced energy incident at the plane boundary of the porous solid. A parameter is used to define the partial opening of pores at the surface of porous solid. An arbitrary value of this parameter allows to study the variations in the energy partition with the opening of surface pores from fully closed to perfectly open. Another parameter is used to vary the saturation in pores from whole liquid to whole gas. Numerical examples are considered to discuss the effects of propagation direction, inhomogeneity parameter, opening of surface pores and saturating pore-fluid on the partition of incident energy.

Propagation of plane harmonic waves through contact with a micro gap

Propagation of harmonic waves through a micro gap between two half-spaces with consideration of smooth contact is studied. When waves which are strong enough strike the surface of one of the solids, the two solids can come into contact and interact locally. By use of Fourier analysis method, the problem is solved analytically; and the gap effects are discussed in detail. The results exhibit some new features induced by the interface contacting. The relation between the higher harmonics and the initial gap width is developed which may be effective on non-destructive testing of a pre-existing gap.

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.

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.

Energy velocity and quality factor of plane harmonic inhomogeneous waves in anisotropic poro-viscoelastic media

SUMMARY Energy flux vector and related wavefield quantities are studied for the propagation of harmonic plane waves in an anisotropic viscoelastic porous medium saturated with viscous fluid. In this dissipative medium, Biot's theory is used to define the propagation of four attenuating waves through different complex-valued slowness vectors. The attenuating waves are considered to be propagating as general inhomogeneous waves. The inhomogeneity strength of an attenuating wave is defined by a non-dimensional parameter. A fixed value of this inhomogeneity parameter is used to calculate the complex slowness vector of any attenuated wave in the medium for an arbitrarily chosen propagation direction. The complex slowness vector is then used to calculate the velocity and direction of energy flux for each of the four waves in the medium. Dissipation of energy is explained in terms of quality factors of attenuation such that the contributions from pore-fluid viscosity and anelastic porous-frame are separated. Deviations of the ray (or group velocity) direction from the propagation direction, the attenuation direction and the propagation–attenuation plane are also calculated. A numerical example is studied to analyse the variations in the energy-flux characteristics with propagation direction and inhomogeneity parameter.

Piezoelectric effect on the velocities of waves in an anisotropic piezo-poroelastic medium

A mathematical model for mechanical and electrical dynamics in an anisotropic piezo-poroelastic (hereafter referred to as APP) medium is solved for three-dimensional propagation of harmonic plane waves. A system of modified Christoffel equations is derived to explain the existence and propagation of four waves in the medium of arbitrary anisotropy. This system is solved to calculate the phase velocities of four waves in an unbounded APP medium. Directional derivatives of phase velocity are derived analytically and are used to calculate the components of the ray velocity vector. A hypothetical numerical model is considered to compute the phase velocity for given (arbitrary) phase direction and then the ray velocity vector. Surfaces are plotted for the phase velocity and ray velocity of each wave in a saturated poroelastic medium in the absence/presence of piezoelectricity. The contributions of the piezoelectric activeness of the solid frame and pore-fluid to the phase and ray velocities are identified and analysed for each of the four waves in the medium.

From the Transport Coefficients of a Relaxation Kinetic Model to Harmonic Wave Solutions

For a gas system of four constituents which experiences the bimolecular chemical reaction A1 +A2 ��A3 +A4, and in a regime close to the chemical equilibrium, the BGK-type model proposed by the authors in a previous paper is here considered with the aim of studying plane harmonic wave solutions to the system of the reactive field equations. The Chapman-Enskog method has been used to determine a first-order approximate solution to the BGK equations, which includes the transport features of shear viscosity, diffusion and thermal conductivity. Such approach leads to the constitutive equations and permits to close the reactive field equations at the Navier-Stokes, Fourier and Fick level. The propagation of plane harmonic waves in a reactive mixture where the transport effects are relevant can then be studied by a normal mode analysis. Numerical results are provided for two different mixtures of the hydrogen-chlorine system where the elementary reaction H2 +Cl ��HCl + H takes place. The behavior of diffusion, shear viscosity and thermal conductivity coefficients, as well as the one of phase velocity and attenuation coefficient, is described focusing the influence of the chemical reaction on the transport properties and harmonic wave solutions.

Analysis of the Effects of Phase-lags on Propagation of Harmonic Plane Waves in Thermoelastic Media

The present paper attempts to investigate the propagation of harmonic plane waves of assigned frequency by employing the thermoelasticity theory with three phase-lags, recently proposed by Roychoudhuri (2007). The solutions of dispersion relation for the longitudinal plane waves are determined analytically and asymptotic expansions of several characterizations of the wave fields- phase velocity, specific loss and penetration depth of the dilatational waves are obtained for both the high frequency and low frequency values. Computational work for numerical values of the above quantities is also carried out with the help of Mathematica. A detailed analysis of the effects of phase-lags on the plane wave is presented by contrasting the theoretical as well as numerical results of the present work with the corresponding results of the theory of thermoelasticity type III (Green and Naghdi, 1993) as reported earlier.

Strong ellipticity and progressive waves in elastic materials with voids

In the present paper, we investigate a model for propagating progressive waves associated with the voids within the framework of a linear theory of porous media. Owing to the use of lighter materials in modern buildings and noise concerns in the environment, such models for progressive waves are of much interest to the building industry. The analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to the industry and medicine. Our analysis is based on the strong ellipticity of the poroelastic materials. We illustrate the model of progressive wave propagation for isotropic and transversely isotropic porous materials. We also study the propagation of harmonic plane waves in porous materials including the thermal effect.

Effects of thermal relaxation time on plane wave propagation under two-temperature thermoelasticity

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.

Wave propagation in transversely isotropic porous piezoelectric materials

Wave propagation in porous piezoelectric material (PPM), having crystal symmetry 6 mm, is studied analytically. Christoffel equation is derived for the propagation of plane harmonic waves in such a medium. The roots of this equation give four complex wave velocities which can propagate in such materials. The phase velocities of propagation and the attenuation quality factors of all these waves are described in terms of complex wave velocities. Phase velocities and attenuation of the waves in PPM depend on the phase direction. Numerical results are computed for the PPM BaTiO 3. The variation of phase velocity and attenuation quality factor with phase direction, porosity and the wave frequency is studied. The effects of anisotropy and piezoelectric coupling are also studied. The phase velocities of two quasi dilatational waves and one quasi shear waves get affected due to piezoelectric coupling while that of type 2 quasi shear wave remain unaffected. The phase velocities of all the four waves show non-dispersive behavior after certain critical high frequency. The phase velocity of all waves decreases with porosity while attenuation of respective waves increases with porosity of the medium. The characteristic curves, including slowness curves, velocity curves, and the attenuation curves, are also studied in this paper.

Reflection and refraction of acoustic waves at poroelastic ocean bed

AbstractOcean bottom is considered as a plane interface between non-viscous liquid and anisotropic dissipative poroelastic solid. The dissipation comes from the viscosity of pore-fluid as well as the anelasticity of the porous frame. Biot’s theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in a porous medium. The non-trivial solution of this system is ensured by a determinantal equation. This equation is solved into a polynomial equation of degree eight, whose roots represent the vertical slowness values for the waves propagating upward and downward in a porous medium. The eight, numerically obtained, slowness values are identified with the four waves propagating towards (or away from) the boundary in the porous medium. Incidence of acoustic wave through the liquid at the interface results in its reflection and the refraction of four attenuating waves in the poroelastic medium. The energy partition among the reflected and refracted waves is calculated at the interface. Conservation of energy is obtained except in the case of partially opened surface pores of the porous medium. Energy refracted to the dissipative porous medium is expressed through an energy matrix. The four diagonal elements of this matrix represent the energy shares of the four inhomogeneous waves and the sum of all the off-diagonal elements of this matrix represents the interaction energy. Few significant results are extracted from the observations in the numerical examples studied. These results represent the effect of anisotropic symmetries, anelasticity, wave-frequency, opening, configuration and flow-impedance of pores, on the energy shares of reflected and refracted waves.

Self-dual electromagnetism

In the first part of this paper, the self-dual formalism is developed for electromagnetic fields in an isotropic, homogeneous, lossless chiral material endowed with the Post constitutive relations. This formalism is afterwards used to analyze harmonic wave propagation in planar and cylindrical waveguides of arbitrary cross section. The second part is devoted to self-dual fields in media with a permittivity variable in a direction. As an application, harmonic plane wave propagation in ionosphere and in a medium with periodic permitivity is analyzed.

Cutoff wave numbers for energy-orthogonal six-node triangular plane-strain elements

This paper studies the propagation of plane harmonic waves in unbounded media discretized by the standard six-node triangular finite element. The element stiffness matrix is split into basic and higher order components which are obtained from mean and deviatoric strain fields, respectively. This decomposition is applied to the elastic energy. Based on the properties of the higher order energy, two values of the wave number are selected. Depending on the desired precision one of those values can be used as optimum cutoff wave number to properly capture a wave field.

Wave propagation in thermoelastic saturated porous medium

Biot’s theory for wave propagation in saturated porous solid is modified to study the propagation of thermoelastic waves in poroelastic medium. Propagation of plane harmonic waves is considered in isotropic poroelastic medium. Relations are derived among the wave-induced temperature in the medium and the displacements of fluid and solid particles. Christoffel equations obtained are modified with the thermal as well as thermoelastic coupling parameters. These equations explain the existence and propagation of four waves in the medium. Three of the waves are attenuating longitudinal waves and one is a non-attenuating transverse wave. Thermal properties of the medium have no effect on the transverse wave. The velocities and attenuation of the longitudinal waves are computed for a numerical model of liquid-saturated sandstone. Their variations with thermal as well as poroelastic parameters are exhibited through numerical examples.

Wave processes in solids with defects

The propagation of plane harmonic waves in viscoelastic and elastoviscoplastic materials are studied using the equations of the field theory of defects, the kinematic identities for an elastic continuum with defects, and the dynamic equations of gauge theory. Wave propagation velocities and refraction and absorption coefficients are determined. The structure of the waves and the correlation between the displacement waves and the defect-field waves determining plastic deformation are analyzed.

Harmonic plane wave propagation in anisotropic chiral media

Harmonic plane wave propagation in anisotropic chiral media