Reflection Phenomena Of Plane Waves Research Articles

Investigating reflection phenomenon of plane waves in a fractional order thermoelastic rotating medium using nonlocal theory

Investigating reflection phenomenon of plane waves in a fractional order thermoelastic rotating medium using nonlocal theory

Reflection of plane waves in a nonlocal double poroelastic semiconducting medium with variable thermal conductivity and mass diffusivity

AbstractThe present investigation is concerned with the reflection phenomena of plane waves in a homogeneous, isotropic, nonlocal, photothermoelastic semiconducting medium under the effects of double porosity, variable thermal conductivity and mass diffusivity. The formulation is applied to generalized thermoelasticity based on the Lord–Shulman theory. The problem is solved analytically and it is shown that there exist six coupled longitudinal waves in addition to an independent transverse wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have been calculated analytically and computed numerically for a specific material with the help of MATLAB programming. The numerical results of reflection coefficients are presented graphically to show the effects of double porosity, photothermal transport process, nonlocality, variable thermal conductivity and mass diffusivity. It is verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence and there is no energy dissipation at the boundary surface. Some special cases of interest have also been inferred from the current investigation.

Propagation characteristics of plane waves in nonlocal isotropic diffusive materials

The size-dependent theoretical modeling of coupled phenomena between deformation and mass diffusion is of current interest in the fields of nanomechanics and nanotechnology. The theory of nonlocal elasticity is applied to study the propagation of plane waves in a linear and isotropic diffusive elastic material. The governing equations of motion are specialized in a plane and are solved for time-harmonic plane wave solutions. The velocity equations are derived to show the possible propagation of three homogeneous plane waves in an isotropic diffusive elastic medium. A reflection phenomenon of plane waves is also considered to obtain the reflection and energy coefficients of reflected waves. A particular numerical example is taken to illustrate graphically the effects of elastic and diffusive nonlocal parameters on the speeds of plane waves, reflection coefficients and energy ratios of reflected waves.

Reflection of plane waves from the boundary of a thermo-magneto-electroelastic solid half space

The theory of generalized thermo-magneto-electroelasticity is employed to obtain the plane wave solutions in an unbounded, homogeneous and transversely isotropic medium. Reflection phenomena of plane waves is considered at a stress free and thermally insulated surface. For incidence of a plane wave, the expressions of reflection coefficients and energy ratios for reflected waves are derived. To explore the characteristics of reflection coefficients and energy ratios, a quantitative example is set up. The half-space of the thermo-magneto-electroelastic medium is assumed to be made out of lithium niobate. The dependence of reflection coefficients and energy ratios on the angle of incidence is illustrated graphically for different values of electric, magnetic and thermal parameters.

Reflection of plane waves on the stress-free and rigid boundary surfaces of pre-stressed piezoelectric-orthotropic substrate: A comparative approach

This study delves with the reflection phenomenon of plane-waves due to incidence of quasi-longitudinal (QL) wave at a semi-infinite structure comprising of pre-stressed piezoelectric-orthotropic substrate (POS) with stress-free (Case I) and rigid (Case II) bounding surfaces. The compact-form expressions of reflection-coefficients (RCs) of reflected QL wave, quasi-transverse (QT) wave and evanescent-electroacoustic (EA) wave for different cases of pre-stressed POS are deduced. To unravel effects of higher anisotropy in substrate, comparative analysis in pre-stressed transversely isotopic piezoelectric substrate (TIPS) medium with stress-free (Case III) and rigid (Case IV) boundaries is carried out. PVDF and ALN materials are considered for numerical computations. For validation, energy-partition and conditions of grazing incidence for all the undertaken cases are analyzed.

Effects of initial stresses on reflection phenomenon of plane waves at the free surface of a rotating piezothermoelastic fiber-reinforced composite half-space

In this paper the impact of initial stresses on reflection characteristics of plane waves at the free surface of a rotating piezothermoelastic fiber-reinforced composite (PTFRC) half-space has been investigated. Three theories of thermoelasticity viz. Green-Lindsay, Lord-Shulman and Classical dynamical coupled theories have been used to explore the problem. The expressions of the amplitude ratios of four types of reflected waves viz. quasi-longitudinal (qP), quasi-transverse (qSV), thermal (T-mode) and electro acoustic (EA) waves have been obtained with the aid of suitable boundary conditions which exhibited their reliance on the incident angle, the properties of the rotating media and varying magnitudes of initial stresses and the impacts of the aforesaid parameters have been extensively studied and demonstrated graphically. Also, the energy ratio of the reflected waves has been derived for different values of initial stresses and it has been showed that the total energy flux at the surface attains value unity.

Propagation of plane waves in an orthotropic magneto-thermodiffusive rotating half-space

The present article is aimed at studying the reflection phenomena of plane waves in a homogeneous, orthotropic, initially stressed magneto-thermoelastic rotating medium with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD) and quasi-transverse wave (qSV) in the medium. The amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The effects of rotation, initial stress, magnetic and diffusion parameters on the amplitude ratios are depicted graphically. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

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.

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

ABSTRACTIn the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.

Effects of voids and rotation on plane waves in generalized thermoelasticity

In the present paper, we study the influence of rotation, thermal and voids parameters on the reflection phenomenon of plane waves in generalized thermoelastic solid with one relaxation time. The governing field equations for isotropic and homogeneous thermoelastic half-space with voids and rotation are formulated in the context of Lord and Shulman theory of generalized thermoelasticity. The solutions of these governing equations indicate the existence of four coupled plane waves, namely; P1; P; P3 and P4 waves in the thermoelastic medium. The boundary conditions at stress-free thermally insulated surface are satisfied to obtain the system of four nonhomogenous equations in the reflection coefficients of various reflected waves for the incidence of P1 wave. A particular material is modeled as the thermoelastic solid half-space to compute the complex absolute values of speeds and reflection coefficients. The speeds and reflection coefficients are shown graphically to observe the influences of rotation, thermal relaxation time and voids parameters.

The reflection phenomena of plane waves at a free boundary in a prestressed elastic half‐space

In this article the reflection phenomena of plane harmonic elastic waves in a homogeneous, prestressed, orthotropic half‐space are discussed. It has been observed that the reflection phenomena of pure mode of P and SV waves in such a medium are different from that of the classical isotropic elastic medium. Apart from the directions parallel to the coordinate axes in the medium there exists a specific direction along which pure modes of P and SV waves may propagate through the medium. It is seen that under certain conditions the P wave propagating in a specific direction will give rise to a reflected wave which is either the superposition of both P and SV waves or an SV wave only, obeying the simple laws of reflection, but it cannot give rise to a pure P mode only. [This phenomenon, i.e., case 3 (as discussed in the paper) may be possible when the denominator of R2 is zero.] Similar phenomena are also observed in the case of an SV wave. Since initial stress generally induces orthotropy in an isotropic medium, similar reflection phenomena should also be observed in a stressfree orthotropic medium. But the reflection pehnomenon of an SH wave is similar to that in the classical elastic medium. Moreover, under equal normal initial stresses, the medium behaves like a classical isotropic one and hence the reflection phenomena are similar to that of the classical case.