Corrected procedure for reflection of harmonic plane waves in a transversely isotropic piezothermoelastic medium: inhomogeneous propagation of incident and reflected waves

2021 ◽  
pp. 1-14
Author(s):  
M. D. Sharma
Keyword(s):  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflected Waves

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-Space

2012 ◽  
Vol 42 (3) ◽  
pp. 33-60 ◽  
Author(s):  
Baljeet Singh ◽  
Anand Yadav
Keyword(s):  
Magnetic Fields ◽  
Half Space ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Thermoelastic Medium ◽  
Reflected Waves ◽  
Velocity Equation ◽  
Thermoelastic Solid

Reflection of Plane Waves in a Rotating Transversly Isotropic Magneto-Thermoelastic Solid Half-SpaceThe governing equations of a rotating transversely isotropic magneto-thermoelastic medium are solved to obtain the velocity equation, which indicates the existence of three quasi plane waves. Reflection of these plane waves from a stress-free thermally insulated surface is studied to obtain the reflection coefficients of various reflected waves. The effects of anisotropy, rotation, thermal and magnetic fields are shown graphically on these coefficients.

The behaviour of elastic surface waves polarized in a plane of material symmetry. I. Addendum

1991 ◽  
Vol 433 (1889) ◽  
pp. 699-710 ◽  
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Point Of View ◽  
Reference Plane ◽  
Material Symmetry ◽  
Reflected Waves ◽  
Inhomogeneous Plane ◽  
Symmetric Surface

This addition to a recent paper by Chadwick ( Proc. R. Soc. Lond . A 430, 213 (1990); hereafter referred to as part I) has been prompted mainly by the discovery of secluded supersonic surface waves propagating in configurations of transversely isotropic elastic media in which the reference plane is not a plane of material symmetry and coexisting with a subsonic surface wave. The occurrence of a supersonic surface wave travelling in a direction e 1 with speed v s implies that there are two homogeneous plane waves, with slowness vectors s i and s r such that s i . e 1 = S r . e 1 = v -1 s , which comprise the incident and reflected waves in a case of simple reflection at the traction-free boundary. Supersonic surface waves may therefore be found by searching within a suitably defined space of simple reflection, R . This is the approach which has led to the new results mentioned above and the principal conclusions of part I are re-examined here from the same point of view. It is found that, whereas the secluded supersonic surface waves in transversely isotropic media correspond to isolated points on a curvilinear projection of R which does not intersect the curve representing subsonic surface waves, the symmetric surface waves studied in part I define a curve which may lie partly inside and partly outside a projection of R in the form of a region, the interior points representing supersonic and the exterior points subsonic surface waves. This discussion is preceded by a simplification of the existence-uniqueness theorem proved in part I and followed by a reconsideration of the possibility that an inhomogeneous plane elastic wave can qualify as a surface wave. Such one-component surface waves do exist, but a symmetric surface wave necessarily contains two inhomogeneous plane waves.

scholarly journals Propagation of plane waves in a rotating transversely isotropic two temperature generalized thermoelastic solid half-space with voids

2016 ◽  
Vol 21 (2) ◽  
pp. 285-301 ◽  
Author(s):  
R. Bijarnia ◽  
B. Singh
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Reflected Waves ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid ◽  
Two Temperature

AbstractThe paper is concerned with the propagation of plane waves in a transversely isotropic two temperature generalized thermoelastic solid half-space with voids and rotation. The governing equations are modified in the context of Lord and Shulman theory of generalized thermoelasticity and solved to show the existence of four plane waves in thex – zplane. Reflection of these plane waves from thermally insulated stress free surface is also studied to obtain a system of four non-homogeneous equations. For numerical computations of speed and reflection coefficients, a particular material is modelled as transversely isotropic generalized thermoelastic solid half-space. The speeds of plane waves are computed against the angle of propagation to observe the effects of two temperature and rotation. Reflection coefficients of various reflected waves are also computed against the angle of incidence to observe the effects of various parameters.

Reflection of Plane Waves in a Rotating Temperature-Dependent Thermoelastic Solid with Diffusion

2012 ◽  
Vol 28 (4) ◽  
pp. 599-606
Author(s):  
B. Singh ◽  
L. Singh ◽  
S. Deswal
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Reflected Waves ◽  
Energy Ratios ◽  
Rotation Parameters ◽  
Thermoelastic Solid

ABSTRACTThe governing equations of a model of rotating generalized thermoelastic diffusion in an isotropic medium with temperature-dependent mechanical properties are formulated in context of Lord-Shulman theory of generalized thermoelasticity. The modulus of elasticity is taken as a linear function of reference temperature. The solution of the governing equations indicates the existence of four coupled plane waves in x-z plane. The reflection of plane waves from the free surface of a rotating temperature-dependent thermoelastic solid half-space with diffusion is considered. The required boundary conditions are satisfied by the appropriate potentials for incident and reflected waves in the half-space to obtain a system of four non-homogeneous equations in the reflection coefficients. The expressions for energy ratios of the reflected waves are also obtained. The reflection coefficients and energy ratios are found to depend upon the angle of incidence, reference temperature, thermodiffusion and rotation parameters. Aluminum material is modeled as the half-space to compute the absolute values of the reflection coefficients and the energy ratios. Effects of temperature dependence and rotation parameters on the reflection coefficients and energy ratios are shown graphically for a certain range of the angle of incidence of the incident plane wave.

Kelvin wave attenuation along nearly straight boundaries

1972 ◽  
Vol 53 (2) ◽  
pp. 273-286 ◽  
Author(s):  
H. G. Pinsent
Keyword(s):  
Incident Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Incident Wavelength ◽  
Reflected Waves ◽  
Linearized Theory ◽  
Coastal Boundary ◽  
Wave Problems

Two related wave problems are considered for a rotating sea of nearly uniform depth bounded by a coastline which is nearly straight. The depth changes are assumed to be independent of the distance from the coastline. The first problem, which is concerned with the origin of Kelvin waves in a coastal wave record, deals with a system of plane waves incident on the coastline and giving rise, in addition to reflected waves, to a Kelvin wave moving along the coast. Linearized theory is used to obtain details of the Kelvin wave for arbitrary perturbations in coastline and depth. Results suggest that the depth changes have their greatest effect in producing Kelvin waves if the incident wave crests are nearly parallel, but not exactly so, to the line of the depth changes. On the other hand when the wave crests are parallel to the coast, Kelvin waves are produced only by changes in the coastal boundary. In the second problem a Kelvin waye is assumed to be the incident wave. To find the energy propagated away from the coastline it is necessary to extend the theory to second order in the perturbations. It is shown that for a fixed wave period less than a pendulum day this energy has a maximum for a perturbation whose length is of comparable magnitude to the incident wavelength. Finally, the theory is applied to Kelvin waves propagating along the Californian coastline. Results obtained tend to confirm the suspicion that coastal irregularities are responsible for certain anomalies detected in tidal wave constituents by Munk, Snodgrass & Wimbush (1970).

scholarly journals Effect of Two Temperatures on Reflection Coefficient in Micropolar Thermoelastic with and without Energy Dissipation Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Rajneesh Kumar ◽  
K. D. Sharma ◽  
S. K. Garg
Keyword(s):  
Energy Dissipation ◽  
Temperature Effects ◽  
Plane Waves ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Reflected Waves ◽  
Two Temperatures ◽  
Thermally Conducting ◽  
Without Energy Dissipation ◽  
Two Temperature

The reflection of plane waves at the free surface of thermally conducting micropolar elastic medium with two temperatures is studied. The theory of thermoelasticity with and without energy dissipation is used to investigate the problem. The expressions for amplitudes ratios of reflected waves at different angles of incident wave are obtained. Dissipation of energy and two-temperature effects on these amplitude ratios with angle of incidence are depicted graphically. Some special and particular cases are also deduced.

Wave propagation in an initially stressed rotating thermo-diffusive medium with two-temperature and micro-concentrations

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Devender Sheoran ◽  
Ramesh Kumar ◽  
Sunil Kumar ◽  
Kapil Kumar Kalkal
Keyword(s):  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Angle Of Incidence ◽  
Amplitude Ratios ◽  
Conservation Of Energy ◽  
Content Type ◽  
Reflected Waves ◽  
Diffusive Medium ◽  
Energy Ratios ◽  
Two Temperature

Purpose The purpose of this paper is to study the reflection of plane waves in an initially stressed rotating thermoelastic diffusive medium with micro-concentrations and two-temperature. Design/methodology/approach A two-dimensional model of generalized thermoelasticity is considered. The governing equations are transformed into the non-dimensional forms using the dimensionless variables. Then, potential functions are introduced for the decoupling of the waves. Further, appropriate boundary conditions are assumed to completely solve the problem. Finally, numerical computations are performed using MATLAB. Findings The problem is solved analytically and it is found that there exist five coupled waves in addition to an independent micro-concentration wave in the considered medium. The amplitude ratios and energy ratios of these reflected waves have also been computed numerically for a specific material. Originality/value The modulus values of amplitude ratios are presented graphically to exhibit the effects of angular velocity, initial stress, two-temperature, diffusion and micro-concentration parameters. The expressions of energy ratios obtained in explicit form are also depicted graphically as functions of angle of incidence. The law of conservation of energy at the free surface during reflection phenomenon is also verified.

The effect of boundaries on wave propagation in a liquid-filled porous solid: III. Reflection of plane waves at a free plane boundary (general case)

1962 ◽  
Vol 52 (3) ◽  
pp. 595-625 ◽  
Author(s):  
H. Deresiewicz ◽  
J. T. Rice
Keyword(s):  
Electromagnetic Waves ◽  
Plane Waves ◽  
Body Waves ◽  
Porous Solid ◽  
Plane Boundary ◽  
Field Equations ◽  
Attenuation Coefficients ◽  
Reflected Waves ◽  
Three Body ◽  
Analytical Expressions

abstract A general solution is derived of Biot's field equations governing small motions of a porous solid saturated with a viscous liquid. The solution is then employed to study some of the phenomena attendant upon the reflection from a plane, traction-free boundary of each of the three body waves predicted by the equations. The problem, though more complex, bears some similarity to that of electromagnetic waves in a conducting medium, in that some of the reflected waves are inhomogeneous, planes of constant amplitude not coinciding with planes of constant phase. Analytical expressions are displayed for the phase velocities, attenuation coefficients, angles of reflection and the amplitude ratios, and explicit formulas are given for the limiting cases of low and high frequencies, representing first-order corrections for porosity of the solid and viscosity of the liquid, respectively. The paper concludes with a presentation of results of numerical calculations pertinent to a kerosene-saturated sandstone.

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